The evacuation of thousands of Americans and their Afghan allies from Kabul would have been “hard and painful no matter when it started or when we began”, Joe Biden insisted on Sunday, amid fierce criticism of his administration’s handling of the US withdrawal.

The Taliban took Kabul a week ago. Biden also said on Sunday the US had now “made a number of changes” to the evacuation effort, “including extended access around the airport and the safe zone”, a move to push back Taliban fighters and lessen deadly chaos around the airport gates.

“We are working diligently to make sure we’ve increased the ability to get [people] out,” Biden said.

The president would not be drawn on tactical details. But he said: “We’ve changed the gate operations and a whole range of things.”

Earlier, the Pentagon activated a rarely used programme to order six US airlines to help move evacuees outside Afghanistan.

US officials also expressed growing concern about a threat from the Islamic State in Kabul, on top of obstacles from the Taliban and bureaucratic problems at home.

Jake Sullivan, the national security adviser, told CNN the threat from Isis was “real, acute, persistent and something we’re focused on with every tool in our arsenal”.

It was a difficult day for Sullivan, the secretary of state, Antony Blinken, and other close aides seeking to defend the administration and explain previous remarks by Biden.

At the White House, Biden said: “The evacuation of thousands of people from Kabul is going to be hard and painful, no matter when it started when we began.”

That, he said, “would have been true if we had started a month ago or a month from now. There is no way to evacuate this many people without pain and loss, or [the] heartbreaking images you see on television. It’s just a fact. My heart aches for those people you see.”

Answering questions, he said it was possible that his deadline for the completion of the evacuation, 31 August, would be extended.

Biden sought to herald an American success, saying that in “a little over 30 hours this weekend” about “11,000 individuals” were evacuated from Kabul. The US, he said, had “evacuated nearly 28,000 people since 14 August in both US and coalition aircraft including civilian charters, bringing the total number of people who were evacuated since July to approximately 33,000”.

The president also said: “We have a long way to go. And a lot could still go wrong.”

Biden said he was open to sanctions on the Taliban after the evacuation was complete, and said he had had “personal contact with the leaders of many countries including Qatar, Germany, Spain, Italy, UAE and others”.

The White House said Afghanistan would be the chief topic of discussion when Biden and G7 leaders meet virtually on Tuesday.

Taliban fighters have made it difficult and dangerous to reach Kabul airport. The British military said on Sunday another seven people had been killed in the crush. The US has given no firm estimate of the number of Americans seeking to leave. Some have put the total between 10,000 and 15,000. Sullivan put it at “several thousand”.

Before Biden spoke, Republicans and other critics stepped up attacks.

Nikki Haley, who was ambassador to the United Nations under Donald Trump when talks with the Taliban began and who hailed Trump’s efforts to withdraw, called Biden’s withdrawal “an embarrassing failure”.

“They surrendered Bagram air force base, which was a major Nato hub,” she told CBS. “They surrendered $85bn of equipment and weapons we should have gotten out of there. They … actually withdrew our troops before they withdrew the American people.”

Ryan Crocker, US ambassador to Afghanistan under George W Bush and Barack Obama, told CBS Biden’s management of the withdrawal was “catastrophic” and had unleashed a “global crisis”.

At the White House, Biden insisted he had simply “decided to end the war”, adding: “You know, we were in Afghanistan [because it was] a place from which [Osama] Bin Laden attacked the United States of America.”

But his previous remarks on that subject produced a difficult experience for Blinken in an interview with Fox News Sunday.

Raising Biden’s remark on Friday that al-Qaida was “gone” from Afghanistan as a result of US actions since 2001, host Chris Wallace said: “A UN report this summer says that al-Qaida is present in 15 of the 34 provinces of Afghanistan. And Gen [Mark] Milley [chair of the Joint Chiefs of Staff] said this summer that if the Taliban … took over Kabul, that he was going to have to upgrade the terror threat from al-Qaida.

“What the president said just wasn’t true.”

Blinken said the US had “diminished the capacity of al-Qaida” to operate from Afghanistan. Wallace repeated his question twice.

Blinken said: “Are there al-Qaida members and remnants in Afghanistan? Yes. But what the president was referring to was its capacity to do what it did on 9/11. And that capacity has been very successfully diminished.”

Wallace also pressed Blinken over Biden’s claim to have seen “no question of our credibility from our allies around the world” since the fall of Kabul, when such questions have been raised in the UK, in Germany and elsewhere.

“Mr Secretary,” Wallace asked. “Does the president not know what’s going on?”

“This is an incredibly emotional time for many of us,” Blinken said, “including allies and partners who have been shoulder-to-shoulder with us in Afghanistan for 20 years at high cost to themselves as well as to us.”

Wallace said he was “not questioning whether or not the allies have a right to complain. I’m not questioning whether or not al-Qaida has a presence. The president said al-Qaida is gone. It’s not gone. The president said he’s not heard any criticism from the allies. There’s been a lot of criticism from the allies.

“Words matter, and the words of the president matter most.”