Britain’s failure to persuade the US to extend the evacuation from Afghanistan into September does not mean the “special relationship” with Washington is over, the foreign secretary, Dominic Raab, has said.

He made the comment in an interview following the virtual G7 summit, which resulted in Joe Biden rejecting calls from the UK and other European partners for the evacuation mission from Afghanistan to be extended beyond 31 August.

In a series of broadcast appearances, Raab also admitted that “with the benefit of hindsight” he should not have been on holiday in Crete when the Taliban were taking over Kabul.

Asked on LBC whether the outcome of the G7 summit meant the special relationship with the US was over, Raab replied: “No, of course it isn’t. It matters a huge amount.”

When it was put to him that Boris Johnson’s conversations with Biden on the evacuation process clearly had not been productive, Raab said that Johnson had been “right to convene the G7 as a whole”.

He went on: “A lot of countries wanted to test: can we have some more days [for the evacuation]. It’s very clear from that we’ll now be working to the end of August.”

Raab faced strong criticism when it emerged that he was on holiday in Crete over the weekend when the Taliban took Kabul. On Wednesday morning he admitted that being away during this period was a mistake.

“Of course, with the benefit of hindsight, I would have wanted to be back in London, but as foreign secretary I’m always able when I’m abroad to respond to a crisis,” he said.

But, in an interview with BBC Radio 4’s Today programme, he refused to comment directly on reports that he stayed in Crete until the Sunday night despite a Downing Street official telling him on Friday that he should return.

Raab reportedly got Johnson to agree that he could stay abroad for an extra two days, but Raab told Today that he did not want to comment on “speculation in the media”.

He also insisted that the idea that he was “lounging on the beach” was “just nonsense”. And reports that he was paddleboarding were also wrong, he said in his interviews.

“The stuff about me paddleboarding, nonsense, the sea was actually closed, it was a red notice. I was focused on the Cobra meetings, the Foreign Office team, the director and the director general, and the international engagement.”

Raab said 9,000 British nationals, and Afghans who had worked for the British, had been evacuated from Kabul since 15 August.

Asked about the Taliban’s declaration on Tuesday that they did not want highly skilled people to leave the country, Raab said if they wanted to avoid this, they would have to run an inclusive administration.

“They’re not going to be able to avoid the refugee crisis by just a few roadblocks, they’re not going to be able to hermetically seal the Afghan border, which is rugged and wide-ranging,” he said.

“If they’re really serious about avoiding the ‘brain drain’ … they’re going to have to find a way to bring in other factions to be more inclusive and to be more moderate compared with the previous Taliban.”

Raab also said the Taliban would have to allow a permissive environment if they wanted international aid to continue.

“If [the Taliban] want aid going into Afghanistan, it won’t go through the Taliban, they’ll have to provide a permissive environment for NGOs [non-governmental organisations] and the UN,” he said.

Raab confirmed that the troops would withdraw by 31 August, but he would not comment on reports that in practice this meant the British civilian evacuation operation would have to end within about 36 hours.

“I’m not going to give the precise timeline,” he said. “The military planners will work out how much time they need to withdraw their equipment, their staff, and what’s really important is we will make the maximum use of all the time we have left.”

After that, he said, Britain would like to see Kabul going back to being a “functional” airport for civilian flights.