There have been calls for the Home Secretary to resign after thousands of people from the Caribbean who had migrated to Britain legally were threatened with deportation.
She described the targets in the inspection report as "local targets used for internal performance management".
James O'Brien had harsh words for Theresa May.
The SNP's home affairs spokeswoman Alison Thewlis also called for Ms Rudd's resignation, saying she was presiding over a department "out of control" and it was "no surprise" targets existed as there was "a litany of callous incompetence" at the Home Office. [The] cruel hostile environment policy by the former home secretary, now prime minister, and continued unabated by the current home secretary.
"We've seen the letters they were sent".
The Home Office subsequently issued an apology to the Windrush generation and said they are highly-valued members of society.
"We don't have targets for removals", Ms Rudd said.
'These were not published targets against which performance was assessed, but if they were used inappropriately then I am clear that this will have to change.
Pressed on the point, she added: "I didn't hear the testimony, I'm not sure what shape that might be in, but if you ask me 'are there numbers of people we expect to be removed?', that's not how we operate".
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"I have never agreed that there should be specific removal targets and I would never support a policy that puts targets ahead of people".
She said the government's net migration target had been "translated down through the operational arm of the Home Office to a.net removals target that enforcement teams have to meet, so they are aiming to remove a certain number of individuals in any given month".
Rudd was forced to return to the House of Commons on Thursday morning to face questions from MPs, who argued she had misled the committee.
Ms Abbott said the revelations were part of a long-running saga of home office mistreatment of migrants, including the Windrush families. I say with all conscience: "is she really the right person to lead this office of state?"
Ms Cooper said the response was a "complete fudge" and she would be writing to Ms Rudd "to get a proper answer" on Thursday.
The report said the target was "not a useful performance measure" due to the varying nature of cases year to year.
There are three types of enforceable departures: deportations, administrative removals, and voluntary departures.
The Guardian's Amelia Gentleman, who uncovered the story of the retired Canadian widow who has lived in the United Kingdom for 44 years before being threatened with deportation, asks the same question on Twitter. Those leaving in this way are able to approach the Home Office for financial assistance with their travel arrangements.
Conservative MP Nicholas Soames said Ms Rudd had "the total support of this side of the house in trying to resolve a very hard legacy issue" to cheers from other Tory MPs.
So far 3,800 calls have been made to the helpline, of which 1,364 were potentially Windrush cases, MPs were told on Wednesday.