After initially rejecting their request for a meeting, a Downing Street U-turn will now see the Prime Minister meet with Caribbean leaders in a bid to ease the controversy.
The Immigration Minister added: "These are people who we welcomed here way back in the '50s and '60s and it's really important to me that we correct any error".
The letter expressed concern about the many long-term British residents who have been incorrectly identified as illegal immigrants.
Ms Rudd was challenged in the Commons over an interview in which Ms Nokes appeared to confirm that some Windrush migrants had been wrongly deported.
It has seen some Windrush generation residents, who might never have applied for United Kingdom passports, left without the documentation now required by officials.
Concerns have been raised following cases where people who came to the United Kingdom as children in the 1950s and 1960s were now facing immigration issues despite having lived in the United Kingdom all their adult lives.
"Frankly, some of the ways they have been treated has been wrong, has been appalling and I am sorry".
The Home Secretary launched an unusual attack on her own department as the Government faced severe criticism over the treatment of the "Windrush" generation of British residents.
The Prime Minister will now meet with the leaders on Tuesday.
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It is estimated as many as 50,000 Windrush generation residents are facing problems.
"Theresa May must apologise for this mess which has taken place as a direct outcome of the hostile environment she created".
After much pressure, Cabinet minister Caroline Nokes admits "terrible mistakes" were made when deporting members of the WIndrush generation. Our Govt invited the Windrush Generation to Britain as citizens to rebuild our country in the wake of WWII.
An online petition calling on the government to allow the "Windrush generation" to stay had gathered more than 85,000 signatures by Monday afternoon.
In a tweet accompanying the article, the Home Office said Nokes "dispels the myth that this government is clamping down on Commonwealth citizens".
According to The Guardian, No 10 Downing Street was asked by representatives of 12 Caribbean countries for a meeting with Theresa May, as part of this week's Commonwealth Heads of Government summit.
However, the Home Office did not keep a record of those granted leave to remain or issue any paperwork confirming it, meaning it is hard for the individuals to now prove they are in the United Kingdom legally.
"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 spokesman said.
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.