The SNP home affairs spokeswoman Joanna Cherry MP said the scandal had been caused by the government's "ludicrous immigration target" and claimed Ms Rudd was being used as a "human shield" to protect Theresa May, the Home Secretary at the time that numerous toughest immigration restrictions were introduced.
Stakeholders will be consulted on the scope of the compensation and on appointing an independent adviser to oversee the scheme, according to the ministry.
The UK Government said yesterday that emigrants to Britain decades ago who have been wrongly targeted over their immigration statuses will be eligible for free citizenship as it tries to contain the continuing crisis.
The secretary said that anyone who had "suffered loss" would be compensated.
Amber Rudd has promised to put right the "unintended and sometimes devastating" harm caused by officials questioning the immigration status of the Windrush generation. "It is shameful that this government has treated this generation in this way".More news: FDA takes actions to restrict kids' access to e-cigs
Shadow Home Secretary Diane Abbott said the situation "should not have been a surprise" given the warnings the government had received.
Ms Rudd said she would act with "urgency and purpose" but sought to blame "successive governments" for failing to ensure they have the documentation they needed.
'It was never the intention that the Windrush generation should be disadvantaged by measures to tackle illegal immigration, ' she said.
The "community grounding" at the Clement Payne Cultural Centre on Crumpton Street, The City, was held to discuss what the organizers described as the "systematic and racist infringement of the civil and human rights" of the Windrush generation.
"This should never have happened", she told MPs. "Of course an apology is just the first step in putting right the wrongs that these people have suffered", she said.More news: Amazon to Offer Package Delivery in Your Car
"An apology is just the first step, ' she insisted, acknowledging the 'devastating" impact on those who can not prove their status.
Ms Abbott drew cheers from the Labour benches after telling Ms Rudd "ultimately the buck stops with her".
Glenda Caesar, who came to the United Kingdom from Dominica with her parents as a six-month-old baby, recently won her battle for citizenship with the Home Office.
In a statement to MPs, she said the £1,330 fees for naturalisation would be waived and applicants would be exempt from needing to pass tests on English language and on their knowledge of life in Britain.
"She is behaving as if it is a shock to her that officials are implementing regulations in the way she intended them to be implemented".More news: Instagram Now Lets Users Download All Photos, Videos With New Tool
Cases have been raised of people who came to the United Kingdom legally as children in the 1950s and 1960s - the so-called Windrush children - facing migration issues despite having lived in the United Kingdom all their adult lives.