The US has so far evacuated more than 3,200 people from Kabul, including 1,100 on Tuesday alone, the White House said, after the Taliban insurgents seized power in Afghanistan.

"Today, US military flights evacuated approximately 1,100 US citizens, US permanent residents, and their families on 13 flights, 12 with C-17 sorties and one with a C-130. Now that we have established the flow, we expect those numbers to escalate," a White House official said on Tuesday.

"We have evacuated more than 3,200 people so far, including our personnel. In addition to these more than 3,200 total evacuated, we have relocated nearly 2,000 Afghan special immigrants to the United States," said the White House official.

Earlier in the day, US National Security Advisor, Jake Sullivan said the issue of evacuation is being resolved with each successive flight.

"We will be putting 300 passengers on an average military cargo plane heading out of the country," he added.

"Second, in terms of people being turned away: By and large, what we have found is that people have been able to get to the airport. In fact, very large numbers of people have been able to get to the airport and present themselves," he said.

"There have been instances where we have received reports of people being turned away or pushed back or even beaten. We are taking that up in a channel with the Taliban to try to resolve those issues. And we are concerned about whether that will continue to unfold in the coming days," Sullivan said.

"As things stand right now, what we are finding is that we are getting people through the gate, we are getting them lined up, and we are getting them on planes, but this is an hour-by-hour issue. It is something we are clear-eyed about and very focused on holding the Taliban accountable to follow through on its commitment," he added.

Sullivan said that the Afghan government and its supporters, including many of the people now seeking to leave, made a passionate case that the US should not conduct a mass evacuation lest they trigger a loss of confidence in the government.

"Now, our signalling support for the government obviously did not save the government, but this was a considered judgment," he added.

Meanwhile, Republican members of the House Foreign Affairs Committee urged President Joe Biden to commit to continuing evacuation flights out of Kabul until all American citizens and all of its Afghan partners are safely out of the country.

"For months, we have consistently urged President Biden and his administration to develop and implement a plan to evacuate our Afghan partners, to secure the US embassy and keep Americans in the country safe, and to manage the impending humanitarian crisis. He ignored us. We are facing this shameful moment in our history because of President Biden's failed leadership. Full stop, they said in a joint statement.

"It is reprehensible that National Security Advisor Sullivan and President Biden are now refusing - repeatedly - to commit to continuing the evacuation of American citizens and our Afghan partners until they are all safely out of the country. We demand President Biden immediately and publicly commit to continuing evacuations for as long as it takes to get all Americans and Afghan allies to safety. Refusing to do so will only serve to further damage US credibility as a partner moving forward," said the Republican lawmakers.

"This is a dire, humanitarian emergency that requires our immediate attention," wrote another group of lawmakers in a letter to Biden.

"We write with great urgency about the rapidly deteriorating situation in Afghanistan. We are gravely concerned for the many people US citizens, Afghan allies and their families, women, NGO employees, journalists, and so many others stuck in Afghanistan fearing for their lives and the future of the country," they wrote.

It is this Administration's moral obligation to leverage all available resources to help as many people as possible to safety in the United States. There is no time to waste, said the lawmakers.

The brutal war in Afghanistan reached a watershed moment on Sunday when the Taliban militants closed in on Kabul before entering the city and took over the presidential palace, forcing embattled President Ashraf Ghani to join fellow citizens and foreigners to flee the country.