Home Secretary Amber Rudd has apologised for not being aware of “specific” migrant removal targets.
The Guardian reported a leaked memo dated last year, which suggested she had been informed of those targets.
In a series of tweets, Ms Rudd said she had not seen this memo and apologised for not being aware of the objectives.
Ms Rudd added she would make a statement to the House of Commons on Monday in response to “legitimate questions” about illegal migration.
A Downing Street spokesman said Ms Rudd retained the “full confidence” of the prime minister.
But Labour’s Shadow Home Secretary Diane Abbott again called for Ms Rudd to resign, saying she was “hanging by a thread”.
BBC political correspondent Alex Forsyth said the home secretary “was not going anywhere tonight” – but added that the pressure on her “was not letting up”.
The Guardian reported that the leaked memo from June 2017, copied to Ms Rudd, set out Home Office targets for achieving 12,800 “enforced returns” in 2017-18. It also said that they had exceeded targets for “assisted returns”.
On Wednesday, the home secretary had told MPs investigating the Windrush scandal there had not been targets for migrant removal.
She later admitted “local” targets had been set before telling the Commons on Thursday she had not been aware of them.
The Windrush row erupted after it emerged some migrants from Commonwealth Caribbean countries who settled in the UK from the late 1940s to the 1970s, and their relatives, had been declared illegal immigrants.
Some of the Windrush generation have been threatened with deportation, lost their jobs, or been refused access to medical treatment.
Ms Abbott said: Ms Rudd’s failure to read “crucial documents” meant she was not aware of targets that have “led to people’s lives being ruined”.
She added: “Another apology is not enough, she should take responsibility for chaos in the Home Office and resign.”
But Cabinet Office minister, and close ally of the prime minister, David Lidington backed the home secretary publicly, tweeting that Ms Rudd had the “determination and resourcefulness” to tackle one of the government’s biggest challenges.
By Jonathan Blake, BBC political correspondent
After an ominous few hours of complete radio silence by the Home Office and Number 10, Amber Rudd tweeted her response to the latest claims about home office targets on illegal migration.
The problem was not the policy. Targets are often used by government departments to monitor performance. Labour had many targets of its own on immigration.
But Ms Rudd has been under pressure because she appeared to be unaware of what her own department was doing.
She has stated her intention to ride out the storm and it has been met with a show of support from Conservative MPs and another statement of “full confidence” from Theresa May.
A cabinet resignation is the last thing the prime minister would want, especially one which would leave Mrs May further exposed to criticism of her record at the home office and with a high profile Remainer on the back benches.
The six-page memo, from Immigration Enforcement Agency boss Hugh Ind, states: “IE has set a target of achieving 12,800 enforced returns in 2017-18, aided by the redistribution of resources towards this area.
“This will move us along the path towards the 10% increased performance on enforced returns, which we promised the home secretary earlier this year.”
It adds: “We have exceeded our target of assisted returns. We set an internal target of 1,250 of these returns for 2016-17… we delivered 1,581.”
In her tweets on Friday night, Ms Rudd said the memo was copied to her office – “as many documents are” – but she didn’t see it.