Downing Street said the prime minister "deeply values" the contribution of Commonwealth citizens who moved to the United Kingdom many decades ago and stressed that nobody with a right to be in the country would be made to leave.
Asked whether people who had been resident in the United Kingdom for decades had been deported, Ms Nokes said: "There have been some horrendous situations which as a minister have appalled me".
"It's disgraceful that the rights of the Windrush Generation have been brought into question by this government and that some have been wrongfully deported", said Jeremy Corbyn, leader of the opposition Labour Party.
The Prime Minister's spokesman insisted she was not aware of the request, which came from 12 Caribbean countries, until this morning.
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 United Kingdom, and is making sure the Home Office is offering the correct solution for individual situations".
"She's 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". Intensifying the row, junior home office minister Caroline Nokes admitted today that some people may have been deported in error.
The letter, written by Labour MP David Lammy, the chair of the all-party parliamentary group on race and community, called on the government to resolve the issue, which Lammy said had caused "undue stress, anxiety and suffering". This is due to changes in immigration rules that require people to provide greater proof of residence to work, rent property or access benefits and some public services. 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".
John Stamos and wife Caitlin welcome their first child together
"Welcome Billy Stamos (named after my father) #NotJustanUncleAnymore #Overjoyed", he captioned a photo of his newborn. The "hncle" part of his post was obviously a joke about his time as Uncle Jesse on his hit show " Full House ".
In an article in The Voice to mark this week's Commonwealth leaders summit in London, the minister said that "the overwhelming majority of the Windrush generation already have the immigration documents they need, but some - through no fault of their own - have not".
"The Government is essentially stripping people of the rights that our Government itself granted decades ago".
She said: "I share the honourable gentleman's admiration for the people who came here from the Caribbean and contributed so much to our society in many many different ways".
Penny Mordaunt, the global development secretary, said there was no "absolutely no question of their right to remain" but admitted the Home Office's handling needed to be better.
'What clearly needs to happen is we need to do a better job with the process that these individuals are having to go through. "We want to give them a message of reassurance because I value these people".
"Having not previously needed documentation they have now found themselves without any way of proving their status today".
Ms Rudd said that fees for sorting out the paperwork of those affected would be waived so that they can have their status confirmed free of charge.