Theresa May is facing renewed pressure from MPs to guarantee the rights of more than three million EU citizens to remain in the UK.
A cross-party committee of MPs, including Michael Gove and other Tory Brexit campaigners, have called on the Prime Minister to guarantee the future rights of EU nationals living in Britain.
In a parliamentary report published on Sunday, the committee said that EU citizens should not be used as “bargaining chips” in negotiations over Brexit.
Mr Gove, the co-chairman of the official Vote Leave campaign, is one of several pro-Brexit Conservative MPs on The Commons Exiting the EU Committee behind the report.
It comes after a vote in the House of Lords last week in which peers defeated the Government by 358 to 256 over the rights of EU citizens.
The peers backed an amendment to the Brexit bill urging ministers to that ensure within three months of article 50 being triggered EU citizens already living in the UK should be given the right to stay.
Ministers have said that while settling the status of EU nationals will be a "priority" in the forthcoming Brexit negotiations they need to be able to secure the rights of UK nationals at the same time.
But the committee said it was "unconscionable" they should have to wait up to two years until the negotiations conclude before their position is clarified.
Committee chairman Hilary Benn said they had been left under a "cloud of uncertainty" and did not want to be used as "bargaining chips" in the talks.
"EU citizens who have come to live and work here have contributed enormously to the economic and cultural life of the UK. They have worked hard, paid their taxes, integrated, raised families and put down roots," he said.
"Although the Government has said it wants EU citizens to be able to remain, this has not offered sufficient reassurance that the rights and status that they have enjoyed will be guaranteed. It should now do so."
Ministers have made clear they intend to overturn the House of Lords vote when the legislation - which authorises the start of the formal Article 50 withdrawal process - returns to the Commons later this month, but they are now likely to face fresh calls to give ground on the issue.
"It would be unconscionable for EU citizens in the UK and UK citizens in the EU not to have clarity about their status for another two years," the committee’s report said.
"We do not believe the electorates of Europe will thank politicians in any country if the situation is allowed to continue."
It added that the current system for EU citizens to apply for permanent residency in the UK - requiring completion of an 85-page form and "copious" supporting evidence - was "not fit for purpose" and needed streamlining "as a matter of urgency".
It warned also that Brexit would not necessarily lead to an immediate fall in net migration into the UK, despite ministers' emphasis on restoring immigration controls.
"An abrupt reduction in the number of EU workers in the UK would cause disruption in a number of sectors. This cannot be the Government's intention," it said.
A Department for Exiting the EU (DExEU) spokeswoman said the Government wanted to "secure" the status of Britons living in the EU and EU nationals in the UK "as quickly as possible".
She added: "It is right to settle this issue on this reciprocal basis. The Government would have liked to have done so already, but some member states have wanted to wait until formal negotiations begin.
"The Bill currently before Parliament has a straightforward purpose - to enact the referendum result and allow the Government to get on with the negotiations - and is not the place to address this issue.
"The Commons passed the Bill without amendment and this should be respected."