Home Secretary Amber Rudd has apologised for being "unaware" of specific migrant removal targets.
Ms Rudd tweeted on Friday that she had not seen a leaked document, published in The Guardian, which suggested she had been briefed on the topic.
It comes as the Home Secretary faces repeated calls to resign over the ongoing Windrush scandal.
Labour leader Jeremy Corbyn has said Rudd's response is "more than odd".
Speaking to ITV News he said: "There's been target figures put up in local offices all over the country of what staff should achieve and then she's telling us there were no targets.
"This is more than odd and so when she makes her statement on Monday, I hope she's going to say because of all this, she's offering her resignation."
The Guardian said the secret internal Home Office document referred to "a target of achieving 12,800 enforced returns in 2017-18" adding “we have exceeded our target of assisted returns”.
According to the paper, the six-page memorandum was prepared by Hugh Ind, the director general of the Immigration Enforcement agency, last June and copied to Ms Rudd, Brandon Lewis, the then immigration minister, as well as a number of senior officials and special advisers.
Ms Rudd tweeted that she "didn't see" the document, but admitted that "legitimate questions" had arisen on the topic.
She also announced that she would make a statement in the House of Commons on Monday.
The latest disclosure comes after Ms Rudd had initially denied targets were used as she was questioned on Wednesday by the Commons Home Affairs committee over the Windrush scandal.
However, she was forced to contradict herself less than 24 hours later after it emerged that a 2015 inspection report said the practice did exist.
Ms Rudd told MPs she had never agreed to using targets to make decisions on migrants' cases.
Home Affairs Committee chairman Yvette Cooper said she would be recalling Ms Rudd to give further evidence over her admission that she should have known about the deportation targets.
"We have obviously been given inaccurate information to Parliament twice now," she told the BBC Radio 4 Today programme.
"This is a serious concern and I am calling Amber Rudd to come back and give further evidence to the committee."
The Home Secretary has faced repeated calls to resign, including from Shadow home secretary Diane Abbott.
She said: “Amber Rudd either failed to read this memo, and has no clear understanding of the policies in her own department, or she has misled Parliament and the British people.
“Either way, she needs to accept responsibility and resign immediately.”
However, Downing Street said the Home Secretary has the "full confidence" of the Prime Minister, while Theresa May's de facto deputy, David Lidington, also publicly backed her.
Environment Secretary Michael Gove also offered his support to Ms Rudd, saying she was "a highly talented and highly effective minister".
According to The Guardian, the memo sent to Ms Rudd said progress had been made on a “path towards the 10% increased performance on enforced returns, which we promised the Home Secretary earlier this year”.
The document, dated June 21 2017, was described as a “summary of performance” by the Immigration Enforcement (IE) agency.
It said that there were 12,503 enforced returns in 2016-17, which was considered a “success given the particularly damaging impact” from the number of late claims for asylum.
The memo goes on: “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.”
The memo then turns to “assisted returns” – which covers cases such as those where an individual has left the country voluntarily on a flight paid for by the British Government.
“Typically these will be our most vulnerable returnees. 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.”
The leak comes after a former head of the UK Border Agency (UKBA) said Ms Rudd’s claim to have not known about the immigration removal targets was “disingenuous”.
Rob Whiteman, who was the chief executive of UKBA from 2011 to 2013, told the BBC Radio 4 Today programme that ministers would have seen internal documents which referred to them.
“Targets are set operationally by managers but, of course, ministers would know there are targets.
“They are intelligent people and they will see performance reports, bids to Treasury for resources, the departmental plan which would cover the targets that are being set for individual services,” he said.
“Fair’s fair, ministers could say we don’t actually set these targets, they are being set by the operations, but I think it is disingenuous, surely, to suggest that they don’t know that they exist because they will have seen them in performance reports and other internal documents.”
MPs are to debate a petition calling for an amnesty for the Windrush generation which was signed by more than 177,000 people.
The Commons Petition Committee announced that a debate on the call for an amnesty “for anyone who was a minor that arrived in Britain between 1948 to 1971” along with Government compensation for “loss and hurt” will be held on April 30 in Westminster Hall.