Theresa May is under renewed pressure on the future of three million EU nationals living in the UK after an influential group of MPs called for their future rights to be immediately guaranteed.
The cross-party Commons Exiting the EU Committee said the Government should not wait for a similar assurance over the British citizens in the EU before acting.
Ministers have said settling the status of EU nationals in the UK will be a "priority" in Brexit negotiations, but they need 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 when the negotiations are completed before their future is clarified.
Hilary Benn, chairman, said EU citizens had been left under a "cloud of uncertainty" and did not want to be used as "bargaining chips".
He said: "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.
"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."
The committee's report adds to the pressure on the Prime Minister following the House of Lords overwhelming backing of an amendment to the Government's Brexit Bill, which calls for a guarantee on the continuing rights of EU citizens.
Ministers have made it clear they intend to overturn the vote when the bill - which authorises the start of the formal withdrawal process - returns to the Commons later this month.
The report states: "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.
"We do not believe the electorates of Europe will thank politicians in any country if the situation is allowed to continue."
The committee said the system for EU citizens to get permanent residency in the UK - completing an 85-page form and "copious" supporting evidence - was "not fit for purpose".
It warned Brexit would also not necessarily lead to an immediate fall in net migration to the UK.