Amber Rudd is facing fresh calls to quit as home secretary after it emerged officials were set targets for the removal of illegal immigrants.
On Wednesday Ms Rudd denied targets were used, when she faced MPs investigating the problems faced by the Windrush generation.
But she admitted on Thursday to "local targets" for "internal" use but said she had not known about them.
The Home Office is now scrapping them, the BBC's Laura Kuenssberg understands.
The instruction to axe them is likely to be sent out from Immigration and Enforcement, a division of the Home Office, in the coming days.
However, the government's overall target of reducing net migration to under 100,000 a year will stay in place, the BBC's political editor said.
Labour's shadow home secretary Diane Abbott said Ms Rudd should resign as a matter of "honour" after confirming the existence of the targets, which union officials have said are prominently displayed on posters at regional immigration centres.
- Who are the Windrush generation?
- Kuenssberg: Who knew what, when?
She told BBC News Ms Rudd was "trying to blame officials" but that was not how the Home Office worked and the "direction will have come from the centre".
She did not see how Ms Rudd could survive in her job, she added, "unless she is only there as a human shield for Theresa May".
Asked how the targets had impacted on Windrush migrants, Ms Abbott said: "Immigration officials may have been looking for soft targets in the shape of West Indian pensioners who don't have hot shot lawyers."
Her Labour frontbench colleague, Dawn Butler, told the BBC's Daily Politics Mrs May was "presiding over a government that has policies that are institutionally racist".
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.
Conservative backbenchers, including Sir Nicholas Soames and Philip Davies rallied behind Ms Rudd, with Mr Davies saying most members of the public backed tougher action against illegal immigration and accused Labour and the SNP of being "out of touch with working class communities".
Answering an urgent question in the Commons, Ms Rudd said: "I have never agreed that there should be specific removal targets and I would never support a policy that puts targets ahead of people.
"The immigration arm of the Home Office has been using local targets for internal performance management.
"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.
"I have asked officials to provide me with a full picture of performance measurement tools which are used at all levels, and will update the House and the Home Affairs select committee as soon as possible."
An inspection report from December 2015, seen by the BBC, showed targets for the voluntary departures of people regarded as having no right to stay in the UK existed at that time.
The Windrush row erupted after it emerged relatives of migrants from Commonwealth Caribbean countries who settled in the UK 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 UK continuously.
Some of the Windrush generation have been threatened with deportation, lost their jobs or been refused access to medical treatment.
Addressing the Home Affairs Select Committee on Wednesday, Amber Rudd said she had asked for more removals of illegal immigrants to take place, but added: "We don't have targets for removals."
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 UK illegally, and staff were under "increasing pressure" to meet it.
There are three types of enforceable departures: deportations, administrative removals, and voluntary departures.
The term "voluntary" describes the method of departure rather than the choice of whether or not to depart, the Migration Observatory explains. Those leaving in this way are able to approach the Home Office for financial assistance with their travel arrangements.
The Green Party has echoed calls for Amber Rudd to quit, saying that her confirmation of the existence of targets had "confirmed our worst fears about the Home Office".
"You can't set targets for people you want to kick out without deciding that some people won't get a fair hearing, because there's a quota to meet by the end of the year," said co-leader Jonathan Bartley.
Lib Dem leader Sir Vince Cable has raised concerns about the Home Office's ability to process applications from millions of EU nationals who want to stay in the UK after Brexit if it cannot deal properly with the Windrush generation.
The government has set up a task force to help those affected by the Windrush cases formalise their status.
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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