The Daily Mail said Foreign, Commonwealth and Development Office officials suggested the foreign secretary talk to Afghan foreign minister Hanif Atmar on Friday – two days before the Taliban marched on Kabul – only for him to be “unavailable” while on holiday.
The paper claimed the Afghan foreign ministry then refused to arrange a call with a junior minister, pushing it back to the next day.
This morning, Labour frontbenchers lined up to criticise Raab, including deputy leader Angela Rayner, who tweeted: "He couldn’t even make one phone call?
"Why is he still in the job this morning?"
Shadow foreign secretary Lisa Nandy said Raab should “be ashamed” to not make the call while he was on holiday in Crete.
She said: “What could possibly have been more important than safeguarding the legacy of two decades of sacrifice and hard-won victories in Afghanistan?
“While the foreign secretary lay on a sun lounger, the Taliban advanced on Kabul and 20 years of progress was allowed to unravel in a matter of hours.
“The foreign secretary should be ashamed and the prime minister has serious questions to answer over why he remains in the job.”
Watch: Raab denies 'lounging' on beach during Taliban takeover
Labour leader Sir Keir Starmer added to the criticism, tweeting: “Who wouldn’t make a phone call if they were told it could save somebody’s life?”
Nick Thomas-Symonds, Labour’s shadow home secretary, said on Twitter Raab’s reported actions were a “dereliction of duty”.
He added: “Failing to make a call has put the lives of brave interpreters at risk, after they served so bravely with our military. Utterly shameful.”
But defence secretary Ben Wallace defended Raab, saying “one phone call is not the reason we are where we are at the moment”.
He added to Sky News: “I have absolutely no idea about what my foreign secretary or any else’s secretary call sheet is like, what I do know is that at no stage in the last few weeks I have (had) a problem with the foreign secretary or anyone else in that department, and in making sure we can process, get people through it.
Wallace said a suggested phone call from Raab to the Afghan foreign minister on Friday would not have made “any difference whatsoever”.
He told Times Radio: “Last Friday, when we were dealing with this, the problem was not whether ministers in the last Afghan government were getting phone calls, as we saw their remit and their power was almost zilch at that moment in time.”
Tory MP David Davis also defended Raab over his holiday, telling Talk Radio he is just "the fashionable target of the month".
He added: "Everyone has the right to family time. It was the government's aggregate failing to grip this issue six months ago."
But a former translator, a British citizen who gave his name as Rafi, 35, told said he was “shocked” if Raab did not make the call.
He added: “How could somebody do something like that in this chaotic situation?
“The interpreters and their families could be killed at any time; the government has bluntly lied to the entire world…
“If he was too busy during his holidays to help, shame on him.”
During Wednesday’s recall of Parliament to discuss Afghanistan, the government confirmed that it will take up to 20,000 people wanting to exit the county as part of its resettlement scheme, with 5,000 due to be accepted in the next 12 months.
The refugee debate comes after No 10 already announced an increase in humanitarian aid for Afghanistan, doubling it to £286 million.
Watch: Starmer slams PM and foreign secretary over Afghanistan response