"The Home Secretary is working hard in order to address the concerns which have been raised in relation to Windrush and to ensure they are addressed and put right".
She vowed to ban them if they were being used "inappropriately".
Addressing the Home Affairs Select Committee on Wednesday, she said she had asked for more removals of illegal immigrants to take place, but was not familiar with a suggestion from a union official that regional targets were in place.
Asked by Labour MP Rachel Maskell who was running the department if Ms Rudd did not know about the targets, the home secretary said: "I accept the criticism on the issue. that's why I'm in the house today setting out the changes I'm going to make.to continue to develop the confidence of everybody involved".
But Rudd's response has been met with calls for her resignation.
Speaking to journalists at a Westminster lunch, the home secretary said: "I have not approved, seen or cleared any targets for removals looking ahead".
United Kingdom home secretary admits to "local targets" for the removal of illegal immigrants.
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During his evidence session earlier this week, Kogan had declined to answer several questions about the NDA he had with Facebook. The past couple of months have seen public calls for people to remove Facebook from their lives.
Labour's Yvette Cooper, chair of the Home Affairs Select Committee, said it was "deeply disappointing" Ms Rudd "did not know the facts" when she gave evidence.
However Ms Rudd, asked if the United Kingdom will stay in the customs union, said: "I won't be drawn on that - we still have some Cabinet discussions to have".
The report said: "For 2014/15 (10 full months) the Home Office set a target of 7,200 voluntary departures, an average of 120 per week, with the weekly target rising to 160 by the end of March 2015".
The spokesman added that the idea of removal targets went back a number of decades under successive governments.
The scandal escalated last week after it transpired that migrants from the Caribbean who settled in the United Kingdom decades ago were asked to prove right to remain in Britain.
The once hotly-tipped candidate to become the next Tory leader now seems to be running around like a chaotic hotel manager not dissimilar to Basil Fawlty, trying to plug holes, self-inflicted from the incompetent running of her Home Office department.
They embarrassingly emerged in a 2015 report this morning, and the disclosure has put more pressure on Rudd to resign over the Windrush scandal and, more broadly, government immigration policy and "hostile environment" created by her predecessor Theresa May.
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I think the IAAF is setting a kind of standard in terms of how they differentiate between men and women and what is acceptable. Other athletes believe she has an unfair advantage because of the high levels of naturally occurring testosterone in her body.
"And they're calling for Amber Rudd to resign for not knowing how bad is the Home Office was under Theresa May".
Voluntary deportation or departure refers to categories of removal where people are subject to enforced removal but may receive assistance from the authorities to leave.
Lucy Moreton, general secretary of the Immigration Service Union, had told the MPs a national target, broken down regionally, had been set to remove people in the United Kingdom illegally, and staff were under "increasing pressure".
Media captionWho are the Windrush generation?
"This country is your home and Britain would not be Britain without you", she said.
So far 3,800 calls have been made to the helpline, of which 1,364 were potentially Windrush cases, MPs were told on Wednesday.
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Another bright spot for Nintendo was the SNES Classic Edition , which Nintendo said "proved to be a hit in every region". Sales for the console are up to 17.79 million as of March 31, according to the company's latest earnings report .