UK armed forces continued to fly embassy staff and dual citizens from Kabul’s international airport on Tuesday, days after the city fell to advancing Taliban fighters.
Speaking to the BBC’s Today radio programme, Mr Raab said the government planned to resettle refugees in the UK through the normal asylum process, as well as “bespoke” initiatives that would be established owing to the crisis.
He would not be drawn on the exact number of migrants expected to enter the UK in the coming weeks and months.
Canada has pledged to take in 20,000 Afghan refugees, while the US is expected to accept 30,000.
After the start of the civil war in Syria and the rise of ISIS, Britain took in about 20,000 vulnerable Iraqis and Syrians fleeing conflict.
Reports suggest the latest concept could be similar, with women with children, people with serious medical conditions and survivors of torture prioritised.
“We’ve always been a big-hearted nation,” Mr Raab said. “We’ve got a model for that, previously used in Syria. So we’re not new to this, but let us work the details through properly and then set it out.”
The priority for now was to secure evacuation for as many British and dual citizens as possible, he said.
At least 150 people made it back to the UK on Sunday and 289 Afghans who served with UK authorities have been flown back on rescue missions in recent days.
Britain would continue to send aid to Afghanistan to “alleviate humanitarian suffering”, but efforts were being made to ensure it did not fall into the Taliban’s hands, Mr Raab said.
“I expect that we will increase our aid budget for development and humanitarian purposes, probably by 10 per cent is what I had in mind," he said.
Mr Raab said the government would engage with the Taliban leadership but would hold it to commitments made in the Doha agreement, under which the militants pledged to prevent Al Qaeda from operating in areas under its control.
Sanctions imposed in conjunction with partners at the UN could be used as “levers” that would hold the Taliban to account if they breached human rights, he said.
“I think it is always important, at least through direct or indirect means, to be able to engage," he said.
"But we will hold the Taliban to the commitments they made in the Doha agreement, commitments never to use their territory, Afghanistan, as a base for terrorism. To have a more inclusive regime going forward.
“They made a range of commitments. Frankly, I can’t tell you that I trust them to follow through on them.”
On Tuesday, a Royal Navy commander overseeing rescue efforts in Kabul said the evacuation was "operating at full pace".
Vice Admiral Sir Ben Key said British forces were working to move between 6,000 and 7,000 people out of Afghanistan.
The security situation was now "much calmer", but he said the evolving political climate meant military teams "can't afford to pause and wait".
"I'm very confident that we now have a stable airfield in which we can get on with the business, alongside all of our allies and partners, that we need to do," he said.
"We will go for as long as it takes us to either meet the demand or when the security situation means that we're no longer operating with consent."
On Monday, Defence Secretary Ben Wallace said the government was processing Afghan asylum claims "as fast as we can" and suggested rules around passports could be relaxed to speed up the process.
The Home Office has said the UK has already admitted more than 3,300 Afghan interpreters, staff and their families for resettlement.
Labour shadow foreign secretary Stephen Kinnock accused Prime Minister Boris Johnson of a “dereliction of duty” and said Britain had a moral obligation to help those in need.
Conservative MP Damian Green said on Twitter that Britain should take in any refugee who could make a case for asylum.
The UK Parliament will be recalled on Wednesday to debate the crisis.
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