Eyewitnesses said the rockets were launched from a car and were aimed towards the airport on Monday morning. It appears Salim Karwan, a neighbourhood adjacent to the airport, was hit in one of the blasts. No one has yet claimed responsibility for the attack.
Smoke could be seen rising above buildings in the north of the city, where the Hamid Karzai international airport is located, and gunfire could be heard after the explosions.
Locals reported hearing the activation of airport's missile defence system, and pictures on social media showed shrapnel falling on to rooftops and the street, suggesting that at least one rocket had been intercepted.
Social media posts, which could not immediately be verified, also showed a vehicle in flames after being apparently struck by retaliatory fire.
In Washington, the White House issued a statement saying President Joe Biden was being briefed on "the rocket attack at Hamid Karzai international airport" in Kabul.
"The president was informed that operations continue uninterrupted at HKIA [Hamid Karzai international airport], and has reconfirmed his order that commanders redouble their efforts to prioritise doing whatever is necessary to protect our forces on the ground," the statement said.
It followed warnings issued by Biden on Saturday that another terrorist attack in Kabul was highly likely in the next 24 to 36 hours. On Thursday, Islamic State, rivals of the Taliban, carried out a suicide bomb attack at the airport that killed more than 150 people, including 13 US troops, and IS militants pose the greatest threat to the final phase of US evacuations.
Biden has set a deadline of 31 August to withdraw all US forces from Afghanistan, drawing to a close his nation's longest military conflict. The UK, Nato and all other western countries ended their evacuation missions over the weekend.
America's top diplomat, secretary of state Antony Blinken, described the final few days as "the most dangerous time in an already extraordinarily dangerous mission".
On Sunday night, a US drone strike blew up a vehicle in Kabul carrying "multiple suicide bombers" from IS before they could attack the ongoing military evacuation at Kabul airport, American officials said. It was the second retaliatory airstrike the US has conducted against the militant group since Thursday's suicide attack.
Despite initial denials by the US that there had any civilian casualties in Sunday's strike, an Afghan official said three children were killed. US officials said the vehicle which was hit had been filled with explosives, causing secondary explosions.
Captain Bill Urban, US central command spokesperson, said: "We are confident we successfully hit the target ... We are assessing the possibilities of civilian casualties, though we have no indications at this time. We remain vigilant for potential future threats."
So far, US evacuation flights have taken more than 114,000 US and Afghan citizens out of Kabul airport, but there are fears that many thousands of vulnerable Afghans who worked for the US and Nato missions have been left behind. The US said they had the capacity to withdraw a final 300 Americans before complete withdrawal on Tuesday.
Biden's national security adviser, Jake Sullivan, said the US does not plan to have an ongoing embassy presence after the final troop withdrawal. But he pledged the US "will make sure there is safe passage for any American citizen, any legal permanent resident" after Tuesday, as well as for "those Afghans who helped us".
The US state department released a statement Sunday signed by about 100 countries, as well as Nato and the European Union, saying they had received "assurances" from the Taliban that people with travel documents would still be able to leave the country.
The Taliban have said they will allow normal travel after the US withdrawal is completed on Tuesday and they assume control of the airport.
Comment: RT reports that IS-K claimed responsibility, claiming to have launched six unguided rockets (at least five of which were reported to have been intercepted by the airport's air defense systems).
Meanwhile on the border with Pakistan, two Pakistani soldiers were killed by militant fire from Afghan militants. The Pakistanis responded, allegedly killing 2-3 and wounding 3 or 4 others (according to their report). TTP (Tehrik-e-Taliban Pakistan) claimed responsibility but denied suffering any casualties.