The new scheme will be aimed at helping those most in need, including women and girls, No 10 says.
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Details of a new resettlement scheme for Afghan refugees are to be announced soon, Downing Street has confirmed.
The new scheme will be aimed at helping those most in need, including women and girls, come to the UK, No 10 said.
It comes after the Taliban seized control of capital city Kabul, prompting thousands to try to flee.
PM Boris Johnson, who has deployed 900 troops to help evacuate British nationals from the country, is to call for a co-ordinated global response.
On Monday evening, the Home Office said the UK had admitted more than 3,300 Afghan interpreters, staff and their families to the UK for resettlement.
The Home Office said “it will be guided by the capacity of local authorities” when deciding how many Afghan refugees to allow to settle in the UK after the Taliban seized power.
Women’s rights activist Malala Yousafzai, who was 15 when she was shot in the head by Taliban militants in Pakistan, urged the international community not to abandon Afghans.
“Countries need to open their borders to Afghan refugees, to the displaced people,” she told BBC Two’s Newsnight.
A Downing Street spokeswoman said the UK team was “working around the clock in incredibly difficult circumstances to help British nationals and as many others as we can get to safety as soon as possible”.
She added that it was “in everyone’s interest not to let Afghanistan fail”.
“That means providing whatever support we can to the Afghan people who have worked so hard to make the country a better place over the last 20 years and who are now in need of our help.”
Foreign Secretary Dominic Raab said earlier that the UK was “looking very carefully at what kind of further commitment we might make”, before adding that the UK was a “big-hearted nation”.
The BBC has been told the new resettlement scheme will be similar to that used to help Syrian refugees in 2014.
Despite chaotic scenes at Kabul airport, the British ambassador to Afghanistan, Sir Laurie Bristow, was still said to be working alongside UK staff and the armed forces to process visas for eligible Afghans who are also being evacuated from the country.
Most Afghan nationals currently eligible for relocation to the UK are those who have worked for the British government in frontline roles “that made a material difference to the delivery of the UK mission” in the country.
This group includes interpreters as well as cultural advisers and embassy staff. Others eligible are those deemed to be at high and imminent risk, according to the MoD.
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Mr Raab said the situation was “not what we wanted, but we have to deal with the new reality”.
He said 289 Afghans who worked with the UK had come to the UK “over the last week”.
The Foreign Office has advised more than 4,000 British citizens thought to be in Afghanistan to leave.
A number of people died at Kabul airport on Monday, as large crowds on the runway led all flights to be halted for several hours.
The Ministry of Defence said no further RAF aircraft were due to depart Kabul on Monday. Another 150 British nationals were due to arrive in the UK from Kabul on Tuesday morning.
On Thursday night, the government announced about 600 UK troops would be sent to the country to help British and eligible Afghan nationals leave.
The MoD said further personnel would be deployed to other countries in the region and able to move on to Afghanistan if needed, while more troops would be put on standby in the UK.
The Pentagon said the US would send another battalion to help, bringing the total US forces on the ground to about 6,000.