Prime Minister Theresa May is to meet counterparts from Caribbean states this week to discuss problems faced by long-term British residents from the Windrush generation over their immigration status, Downing Street has announced.
Mrs May's official spokesman said the PM was clear that nobody with a right to be in the UK would be made to leave.
The announcement came amid growing anger about individuals facing the threat of deportation and being denied access to healthcare due to UK paperwork issues and anomalies affecting some immigrants who arrived between the late 1940s and early 1970s.
Reports suggested that Mrs May had rejected a request from 12 Caribbean leaders to discuss the issue.
But Number 10 said that the PM only became aware of the request on Monday morning and hoped to meet as many of them as possible for a meeting this week, while they are in London for the Commonwealth summit.
Mrs May's official spokesman said: "She deeply values the contribution made by these and all Commonwealth citizens who have made a life in the UK, and is making sure the Home Office is offering the correct solution for individual situations.
"She is aware that many people are unlikely to have documents that are over 40 years old and she is clear that no-one with the right to be here will be made to leave."
The announcement came after a cross-party group of 140 MPs wrote to Mrs May calling for an "immediate and effective" response to problems faced by members of the Windrush generation.
The letter to the PM was co-ordinated by David Lammy, chairman of the Race and Community All Party Parliamentary Group, and has the backing of Labour leader Jeremy Corbyn and Conservative MPs such as Sarah Wollaston.
The letter to Mrs May calls for action over the immigration anomalies, stating: "All too often these routine bureaucratic errors bring about the separation of families and irreparable damage to lives in addition to undue stress, anxiety and suffering.
"The impact has been felt in the cases of individuals losing the right to work, to rent property, to receive pensions, to access their bank accounts or even to access vital healthcare - a particularly cruel twist of fate as so many of those affected have spent their lives in the service of our National Health Service."
Mr Lammy said: "What is going on is grotesque, immoral and inhumane. It is a stain on our nation's conscience and the Prime Minister must act urgently to right this historic wrong.
"After World War II we invited the Windrush generation over as citizens to help rebuild our country, and now their children are being treated like criminals.
"The Government is essentially stripping people of the rights that our Government itself granted decades ago.
"The Government must immediately guarantee that anyone who comes forward to clarify their status should not face deportation or detention, because as things stand today there are thousands of people who are too worried about their future to come forward."
International Development Secretary Penny Mordaunt told BBC Radio 4's Today programme: "People who are in that situation, there is absolutely no question of their right to remain, and their right to gain access to services such as healthcare.
"What clearly needs to happen is we need to do a better job with the process that these individuals are having to go through.
"People should not be concerned about this - they have the right to stay and we should be reassuring them of that."
Barbados High Commissioner Guy Hewitt told the BBC: "Because they came from colonies which were not independent, they thought they were British subjects.
"They thought that there was no need for them to regularise their status.
"And 40, 50 years on are being told by the Home Office not that they are just anomalies, but they are illegal immigrants. They are being shut out of the system.
"Some have been detained, are still being detained. Others have been deported."