For almost two weeks, British ministers have been struggling to explain why some descendants of the "Windrush generation", who were invited to Britain to plug labour shortfalls between 1948 and 1971, had been labelled illegal immigrants.
Ms Rudd's appearance in the Commons followed an appearance before the home affairs select committee, where she was asked whether her department had regional targets, after an immigration union official claimed they existed.
Ms Rudd told the Commons Home Affairs Committee that she had known about the problem for months and said officials were still checking how many people had been detained over their supposed immigration status.
She has now admitted to "local targets" for "internal performance management" but said she was not aware of them. When her spokesman was asked if PM had full confidence in Rudd after Windrush, he told media: "Yes".
She also faced fierce condemnation from Labour's Yvette Cooper, who accused the Home Office of a "complete fudge" over its response to perceived immigration targets.
"I do think", she said stoutly, to Tory cheers and Labour disbelief, "that I am the person who can put this right".
Some of the Windrush migrants have been made homeless, lost their jobs, threatened with deportation and denied benefits, according to the Guardian newspaper.
Asked whether she regarded herself as a future leadership contender, she said: "I'm pretty much focused on what I have got to do now".
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Williams told MPs on the committee that the Home Office since 2008 had been moving away from interviewing applicants in the case of economic and student migration, towards greater use of "prescriptive lists of documents", in order to make the process more objective.
The report said the target was "not a useful performance measure" due to the varying nature of cases year to year.
"But if they were used inappropriately then this will have to change".
"We now understand that people have been removed because of targets and she says she didn't know".
The Windrush row erupted after it emerged relatives of migrants from Commonwealth Caribbean countries who settled in the United Kingdom from the late 1940s to the 1970s had been declared illegal immigrants if they could not provide a range of documentation which proved they had lived in the United Kingdom continuously.
Ms Rudd responded by saying: "I believe I have addressed the issue of targets, referring to the fact that there are some offices which are working with them".
Prime minister Theresa May's spokesman insisted removal targets was a concept which "goes back over a number of decades", and cited ones imposed by Labour governments from 1998 to 2010, although these were aimed at more specific areas such as asylum seekers and foreign prisoners.
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.
"This country is your home and Britain would not be Britain without you", she said.