Amber Rudd has been summoned back to Parliament under mounting pressure after twice appearing to give MPs false information.
She is due to give a statement in the House of Commons on Monday in which she is likely to again apologise for claims she made about the government's use of deportation targets.
Yvette Cooper, the chair of an influential parliamentary committee, said she had also asked the beleaguered home secretary to answer MPs' questions amid "serious concern" over the accuracy of her previous statements.
Ms Rudd is facing continued calls to resign over her handling of the Windrush scandal.
Ms Cooper said she had asked Ms Rudd to reappear in front of the Home Affairs Select Committee to explain why she had appeared to be unaware of her department's policy of imposing numerical targets for deportations.
Ms Rudd has initially told the committee the Home Office did not use targets for deportations, only for this to later be proved untrue. She then claimed she had been unaware of the targets but this too prompted questions when a leaked memo revealed details of the policy had been sent to her office.
Ms Cooper told the BBC Radio 4 Today programme: "We have obviously been given inaccurate information to Parliament twice now.
"This is a serious concern and I am calling Amber Rudd to come back and give further evidence to the committee.
"I think we will also want to hear from the permanent secretary as well, because this raises some questions about the way the Home Office is operating."
As she fought to cling on to her job, Ms Rudd used a series of tweets to respond to the leaked memo - around nine hours after it was originally published.
She wrote: "I will be making a statement in the House of Commons on Monday in response to legitimate questions that have arisen on targets and illegal migration.
"I wasn't aware of specific removal targets. I should have been and I'm sorry that I wasn't. I didn't see the leaked document, although it was copied to my office as many documents are.
"As home secretary I will work to ensure that our immigration policy is fair and humane."
Labour re-iterated its calls for Ms Rudd to quit over the issue.
Diane Abbott, the shadow home secretary, told Today: "I am just surprised that she doesn't seem to take the issue seriously enough to offer her resignation.
She added: "Nobody, least of all the communities and the Windrush victims, is going to take the government seriously on this issue until Amber Rudd offers her resignation.
Ms Abbott said the decision to set a "broad numerical target" could have been a factor behind the Windrush scandal, which saw people who have lived in the UK for decades losing jobs, pensions and healthcare and being threatened with deportation.
"It wasn't saying, for instance, we have to have a target for deporting former criminals. The danger is that that very broad target put pressure on Home Office officials to bundle Jamaican grandmothers into detention centres," she said.
But Ms Rudd's cabinet colleagues rowed in behind her, suggesting the memo in question had not been put in the "red box" of documents that ministers are given to read each day.
Michael Gove, the environment secretary, said: "When documents that should be placed in front of a home secretary aren't then placed in front of a home secretary, that is sad, that is regrettable.
"But she was very clear both in her apology and also in the fact that this specific document wasn't placed in her box, wasn't brought to her attention. It wasn't a matter for decision. It was specifically prepared for another minister. It was sent to his office. It was copied in to the home secretary's office.
Calling Ms Rudd a "highly talented and highly effective minister", he added: "There are hundreds of documents which are copied in to a secretary of state's office every day and week. Some of those documents are not then brought to the secretary of state's specific attention."
David Gauke, the justice secretary, said: "She has accepted that she made a mistake. She didn't knowingly mislead the House of Commons but she accepted that she was inaccurate in her statements," he told the BBC Radio 4 Today programme.
"She is coming back to the House of Commons on Monday to correct the record.
"I have worked closely with Amber. I think she is an excellent home secretary and I look forward to working with her in future."
Downing Street also insisted Theresa May had full confidence in Ms Rudd.
“The PM has full confidence in the home secretary, and the hugely important work that she is carrying out at the Home Office," a spokesperson said.
