In 2000, Putin's hard line against religious separatism became a leading factor in his electoral victory.
On September 4th, Russia's President Vladimir Putin restated, as he has many times before, that he seeks a U.S.- Russian alliance to overcome the global Islamic jihad movement, in Syria, Iraq, and everywhere.

Then, on Tuesday September 8th, Yahoo News bannered, "Austria joins growing voices that say Assad must be part of Syrian solution," and reported that Austria's Foreign Minister Sebastian Kurz said: "In my opinion the priority is the fight against terror. This will not be possible without powers such as Russia and Iran." German Economic News noted then that, "Spanish Foreign Minister Jose Manuel Garcia Margallo had already called on Monday for negotiations with Assad to end the war."

However, the U.S. government is strongly opposed to accepting Putin's offer of an alliance to overcome Islamic jihad.

Putin's foreign-policy objectives are consistent; and his latest turn fits with all that has preceded, which has been his single-minded focus, ever since he first became Russia's leader in 2000: to defeat the global threat of Islamic jihad, which has been the chief military concern for Russia itself, ever since the First Chechen War, during 1994-96, radicalized the predominantly Sunni (Saudi-based) Muslim Chechen Republic, to separate themselves from the predominantly Orthodox Catholic Russia. By the time of Putin's contest for the Presidency in 2000, Putin's hard line against religious separatism became a leading factor in his electoral victory.

Comment: Unlike the US, living in its reality bubble and (so far) not experiencing the consequences of its global meddling, Putin has had real, hard experience with religious terrorism.

On 11 February 2004, this is how the pro-Western Moscow Times, which wikipedia refers to as "the first Western daily to be published in Russia," described "Putin and the Chechen War: Together Forever":
In the summer of 1999, the ruling elite was at a loss. Boris Yeltsin was clearly not up to running the country, but no suitable successor could be found. The obvious candidates — Sergei Stepashin, Nikolai Bordyuzha and Sergei Kiriyenko — weren't presidential material. But then Chechen separatists staged a raid into neighboring Dagestan. Putin directed the operation that drove the fighters from Dagestan, and after two apartment buildings were blown up in Moscow [which some accounts say was secretly planned by Putin himself], Putin launched an "anti-terrorist operation" in Chechnya. Suddenly Putin was the No. 1 politician in the country. ...

The Chechen fighters were operating on the assumption that the Kremlin would not tolerate substantial losses on the eve of the election. This is why Chechen detachments flouted military logic and remained in Grozny after it was surrounded, continuing to offer fierce resistance.

Putin's campaign managers also assumed that heavy Russian losses would hurt his chances at the polls. As the fighting in Grozny took its toll, they feared that by election day in June 2000 Putin's support would have evaporated. This concern probably explains Yeltsin's decision to step down early, bringing the election forward by several months.

As we now know, those fears were groundless. Heavy Russian losses had no impact on Putin's poll numbers. The four years of Putin's first term, during which the war raged on unabated, have made clear that Russian voters are prepared to endure endless lies from their leaders about the latest "phase" of the "operation" in Chechnya, as well as a staggering number of Russian dead.

[Alexander Golts] doubt that any Russian politician today would have the nerve to remind Putin of the promises he made back in 2000. He vowed "to crush the terrorist scum'.
chechnya peace
Chechnya after transformation of the war-ravaged city. Peaceful, quiet, prosperous after terrorists were routed in the 2nd Chechen war.
However, Simon Shuster, who likewise is anti-Putin, had this to say about Chechnya, in the cover story of TIME, eleven years later, on 22 June 2015:
Chechnya has undergone a striking transformation. Its cities have been rebuilt with money from Moscow. All traces of its separatist rebellion have been suppressed. And most importantly, a new generation has been raised to respect—at times even to worship—the Russian leader and his local proxies. With no clear memories of the wars for independence, the young people of Chechnya are now the best guarantee that Russia's hold over the region will persist.
Putin might not have "crushed the terrorist scum," but he has held it at bay for long enough a time to reestablish relative peace in Chechnya, along with a previously unparallelled degree of prosperity.

The International Crisis Group, a pro-Western and anti-Russian NGO, and an affiliate of NATO's Atlantic Council, vigorously criticizes the authoritarianism and cult of personality that Putin has imposed in Chechnya, even while reluctantly acknowledging that:
The number of Chechens in the insurgency has been steadily decreasing. With their centuries-long record of being ready to die for their independence, Chechens do not seem very susceptible to the suicidal ideology of a global jihad. Many who are have joined the conflict in Syria, which has significantly drained the human resources of the North Caucasus insurgency overall, but especially in Chechnya. A Chechen interior ministry source estimated in 2013 that 200-500 Chechens were fighting in Syria.
The Islamic jihadists are more comfortable in, and more accepted by the residents of, the anti-Assad, pro-Sunni, areas of Syria, doing war against Shiia Muslims, and against the Russian-supported secular Shiia President Assad, than they are back home in their native land (Chechnya in Russia). Even Putin's enemies acknowledge Putin's successes against the Saudi-based Sunni international Islamic jihad movement. Putin has become an experienced specialist in the war against Islamic terrorism.

Whereas the United States simply spreads Islamic jihad, even while bombing jihadists and creating more martyrs for "the cause" of jihad, Russia has found ways instead to push back effectively against the Saudi-originated movement of Islamic jihad, and to develop, during decades, a peaceful regional diversity, which can encompass even areas where (as in Chechnya) Islamic or sharia law is imposed, and do this even within a predominantly Christian-majority nation (such as Russia, but this also describes the United States).

The U.S. never had to deal with the challenge that Russia has, of containing within itself a majority-Muslim state, and especially not containing a state whose majority are Sunni Muslim, the variant of Islam that (unlike Shiia Islam) produces jihadists, people with suicide-belts etc., who seek to impose a global Caliphate, a worldwide regime that imposes strict Islamic law.

The ICG report on Chechnya criticizes today's Chechnya, by saying that, "Much of the population lives off pensions and welfare payments," and that corruption and clan-rule are the norm, but all that's really new in this is actually the peace, and the pensions: corruption and clan-rule have been the rule in Chechnya for centuries, at the very least.

Simon Shuster's video at TIME, about today's Chechnya, opens:
The kids growing up in Chechnya these days are a lot luckier than their parents and their grandparents. At least the youngest ones have only known their homeland to be a peaceful and even quite beautiful place, full of enormous mosques, and skyscrapers, and shopping districts, and fast-food joints.
Shuster then refers to the civil war, but he says, "Today, Chechnya is a very different place," and he acknowledges that the adults there, who remember the wars, are much happier now, that the jihadists are gone, or dead.

Al Jazeera television, which is controlled by gas-rich Qatar's anti-Russian Sunni royal family, the Thanis, has criticized Putin for his placing in control of Chechnya the anti-jihadist Chechen Muslim, Ramzan Kadyrov. Thanis are also the chief financial backers for the Muslim Brotherhood, and, along with the Saud family (the main financial backers of Al Qaeda), are also among the main financial backers of the Syrian warriors who are fighting to replace the secular Shiite leader, Assad, by a sectarian Sunni Islamic regime in Syria.

The anti-Russian American newspaper, New York Times, headlined on 1 July 2004,"Qatar Court Convicts 2 Russians in Top Chechen's Death," and reported:
The trial has provided an international stage for both sides to air their grievances about Russia's war in Chechnya and debate the question of whether the fight against terrorism justified such extreme measures. Among those in the courtroom on Wednesday was Akhmed Zakayev, a leader of Chechnya's separatist movement, who has successfully challenged efforts by Russia to extradite him. Mr. Zakayev said in a telephone interview that the killing of Mr. Yandarbiyev showed that Russia under Mr. Putin had reverted to the darkest tactics of its Soviet past, when K.G.B. agents tracked down enemies of the state overseas.
In U.S.-allied nations generally, anti-Russian jihadists have, to a large extent, been sympathetically received, and favorably reported (as in that cited NYT article).

So: Regardless of Putin's success at dealing with Islamic jihadists, his invitation to the United States to work together to defeat the Sunni, and mainly Saudi and Thani-funded, international movement for Islamic jihad for a global Caliphate, will probably continue to meet only America's cold shoulder. The United States opposes Islamic jihad, but it opposes Russia more.

Or, at least, the U.S. Government does. Obama primarily seeks to defeat Russia, not to ally with it — not even against Islamic jihad.

Investigative historian Eric Zuesse is the author, most recently, of They're Not Even Close: The Democratic vs. Republican Economic Records, 1910-2010, and of CHRIST'S VENTRILOQUISTS: The Event that Created Christianity.