Home Secretary Amber Rudd is facing fresh calls to quit after a leaked memo suggested she had been informed about immigration removal targets.
The home secretary had initially told MPs probing the Windrush scandal there were no targets - before admitting "local" targets had been set.
She told the Commons on Thursday she had not been aware of them.
But the Guardian has reported a June 2017 memo from an official, copied to Ms Rudd, that refers to targets.
Labour's shadow home secretary Diane Abbott 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."
But Conservative vice-chair Kemi Badenoch backed Ms Rudd.
"Aside from this issue, she has been doing a good job," the MP for Saffron Walden told Radio 4's Any Questions.
"She's apologised, she's taken action to deal with it swiftly. And also, we have an immigration bill that's coming later in the year - she's the only person who can drive this forward."
By BBC political correspondent Jonathan Blake
The problem is not the policy. Targets are often used by government departments to monitor performance. Labour had many targets of its own on immigration.
But Amber Rudd was already under pressure because she appeared to be unaware of what her own department was doing.
The Guardian has now published a leaked memo suggesting she was told of immigration removal targets.
This is despite her previously telling MPs that "we don't have targets for removals."
A resignation issue, according to Labour.
But removing Amber Rudd from office would leave the prime minister further exposed to criticism of her record at the Home Office and put a high-profile Remainer on the backbenches.
So whether the home secretary stays in her job may well be a matter for Amber Rudd to decide for herself.
The Guardian reports that 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."
The Guardian says the memo was copied to Ms Rudd and then-immigration minister Brandon Lewis, as well as some civil servants and advisers.
On Friday, Rob Whiteman, who was chief executive of the UK Border Agency from 2011 to 2013, told the BBC all public services operated on targets and "of course" ministers would be aware of them.
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."
Ms Rudd has been under pressure over the issue of targets this week, having initially told the home affairs select committee on Wednesday: "We don't have targets for removals."
But an inspection report from December 2015 emerged, showing targets for the voluntary departures of people regarded as having no right to stay in the UK existed at that time.
On Thursday, Ms Rudd told MPs: "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."
On the issue of targets, she added: "Unfortunately, I was not aware of them, and I want to be aware of them, which is why I am now putting in place different measures to ensure that that happens."
The home secretary has faced calls to quit from Labour, the SNP and the Green Party, following her admission that the targets did exist and, according to union officials, are prominently displayed on posters at regional immigration centres.
But Conservative backbenchers, including Sir Nicholas Soames and Philip Davies, rallied behind Ms Rudd on Thursday, with Mr Davies saying most members of the public backed tougher action against illegal immigration.
The Windrush row erupted after it emerged migrants from Commonwealth Caribbean countries and their relatives 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 that 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.