Joe Biden, under mounting pressure to evacuate American citizens from Afghanistan, has said the US is considering “every means” to get people to Kabul airport, promising: “We will get you home.”

The embattled president again defended his decision to end the 20-year intervention by withdrawing US forces, which resulted in the Afghan government’s total capitulation to the Taliban, and denied that it hurt Washington’s standing with allies.

Media reports from Kabul have described outbursts of chaos and violence in which Taliban guards refuse to let anyone, including those with American passports, past checkpoints near the airport. The US embassy in Kabul has also told American citizens that the government “cannot ensure safe passage to the airport”.

But speaking at the White House on Friday, Biden insisted: “Let me be clear. Any American who wants to come home, we will get you home.”

However, he then acknowledged: “Make no mistake, this evacuation mission is dangerous. It involves risks to our armed forces and it’s being conducted under difficult circumstances.

“I cannot promise what the final outcome will be or that it will be without risk of loss. But as commander-in-chief, I can assure you that I will mobilize every resource necessary.”

After the most turbulent week of his presidency, Biden spoke in the East Room flanked by Vice-President Kamala Harris, the secretary of state, Antony Blinken, defence secretary, Lloyd Austin, and national security adviser, Jake Sullivan.

He said 18,000 people had been evacuated since July, and 13,000 since the military airlift began on 14 August, along with “thousands more” on charter flights. About 5,700 evacuees were moved out on Thursday.

Biden added that the US was in “constant contact” with the Taliban to enable Americans to reach Kabul airport. His administration had seen “no indication” that Americans are having trouble, he continued, pointing to an agreement with the Taliban to allow US citizens to go through checkpoints.

“We know of no circumstance where American citizens carrying an American passport are trying to get through to the airport, but we will do whatever needs to be done to see to it they get to the airport.”

Earlier this week an elite team of French police officers deployed in Kabul to transport people to the city’s airport for evacuation, according to the Washington Post, which noted similar reports of British and German forces intervening on behalf of their nationals and allies.

Asked if he would consider rescue operations for Americans and Afghan allies trapped behind Taliban checkpoints, the president replied: “We’re considering every opportunity and every means by which we could get folks to the airport.”

At one point, he said, US forces went outside the gate to the airport and brought 169 Americans over the wall. But expanding the perimeter of the safe zone beyond the airport would “be likely to draw an awful lot of unintended consequences”, he warned.

The White House admits it does not know how many Americans remain in Afghanistan.

Biden also vowed to continue evacuating thousands of Afghans who supported the US forces as well at-risk groups including female leaders and journalists. The White House worked with the New York Times, Wall Street Journal and Washington Post to “successfully” evacuate 204 of their employees from the country.

“We’re going to do everything, everything that we can to provide safe evacuation for our Afghan allies, partners, and Afghans who might be targeted because of their association with the United States.”

The US has 6,000 troops at the airport but they are scheduled to leave by the end of the month. Biden said: “This is one of the largest, most difficult airlifts in history, and the only country in the world capable of projecting this much power on the far side of the world with this degree of precision is the United States of America.”

America’s bungled withdrawal, and the shocking speed of the Taliban takeover, has prompted fierce criticism at home, including from some Democrats, as well as from politicians overseas. Analysts suggest it will only serve to embolden adversaries such as China and Russia.

But Biden said: “I have seen no question of our credibility from our allies around the world. I’ve spoken with our Nato allies … The fact of the matter is I have not seen that – matter of fact the exact opposite I’ve gotten. Exact opposite thing is we’re acting with dispatch, we’re acting, committing to what we said we would do.”

He justified the withdrawal by noting that estimated costs of America’s longest war vary from $1tn to $2tn and that the terrorist threat has now metastasised, with the Islamic State and al-Qaida posing a greater danger than the Taliban. “This is where we should be. This is about America leading the world and all our allies have agreed with that.”

During the exchange with reporters, he also commented: “There’ll be plenty of time to criticise and second-guess when this operation is over.”

But as evidence grows that the Taliban is crushing internal dissent with lethal force, and hunting down people who worked with the US or Afghan government, the criticism is well under way.

Emma Vaughn, a spokesperson for the Republican national committee, responded to his remarks by stating: “Joe Biden created a disaster in Afghanistan, and Americans and our allies are paying the price.

“Biden’s claims that Americans can safely get to the Kabul airport and that our allies support his management handling of the crisis are verifiably false. Americans deserve accountability and transparency, not continued lies and failure.”

Daniel DePetris, a fellow at the Defense Priorities thinktank, said: “The scenes from the airport in Kabul are heart-wrenching. While the US evacuation process has been less than ideal, the case for withdrawing all US troops from Afghanistan is just as strong today as it was over a decade ago. There are no longer any vital US interests at stake.”