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In his second address here to the U.S. State Department since taking office, Tillerson also said the U.S.-Russian relationship was the lowest since the Cold War.
"I characterized to President Putin (of Russia) our relationship was the lowest since the Cold War," said Tillerson. "He did not disagree."
According to Tillerson, Washington and Moscow were working to see if trust could be rebuilt by starting one issue at a time.
"We need to stabilize the relations that are spiraling down," said Tillerson.
Tillerson's remarks came one day after U.S. President Donald Trump and his Russian counterpart Vladimir Putin talked by phone for the first time since the two governments wrangled over a U.S. strike on Syrian government last month.
According to a White House readout of the call, the conversation was a "very good one," and included the discussion of safe, or de-escalation, zones in Syria to achieve lasting peace for humanitarian and many other reasons.
The two leaders also discussed "at length working together" to fight terrorism across the Middle East and "the very dangerous situation" in the Korean Peninsula.
Trump on April 6 ordered a targeted missile strike at a Syrian military airfield in response to a chemical weapons attack in the rebel-held Syrian town of Khan Sheikhoun allegedly launched by the Syrian government.
After the U.S. strike, Syrian state TV called the assault an "aggression" and both Russia and Syria had denied that the Syrian government launched the chemical weapons attack.
The Russian government also condemned the U.S. strike against the Syrian government as "aggression against a sovereign state in violation of international law."
After the incident, Trump told reporters last month that the United States is "not getting along with Russia at all" and the relations between the two countries "may be at an all-time low."
Comment: Further reading: Reconciliation back on the table? Lavrov & Tillerson to meet next week