Theresa May has defended targets for the removal of illegal immigrants as she confirmed the practice was in place when she was home secretary.
Members of the public want the Government to deal with people who have no right to be in the country, the Prime Minister insisted.
But Jeremy Corbyn insisted Mrs May had "questions to answer" about her time in the Home Office.
Mrs May made Sajid Javid Home Secretary after Amber Rudd quit, admitting she "inadvertently" misled MPs over Government targets for removing illegal migrants.
During a local election campaign visit to Greater Manchester, Mrs May said: "When I was home secretary, yes, there were targets in terms of removing people from the country who were here illegally.
"This is important. If you talk to members of the public they want to ensure that we are dealing with people who are here illegally."
Mr Corbyn said Ms Rudd had been the "human shield" for the Prime Minister.
The Labour leader said Mrs May "now has questions to answer" about "what she actually did as home secretary".
"She was presiding over, in her terms, the creation of a hostile environment," he said.
As well as the row over targets on migrant removals, Ms Rudd had also been battling intense criticism over the Windrush scandal, which has seen people from a Caribbean background denied access to benefits and healthcare or threatened with deportation despite decades of residence in the UK.
She became the fifth enforced departure from the Cabinet since last year's snap general election and stepped down the evening before she was due to make a statement in the House of Commons.
Mr Javid vowed to make sure people caught up in the Windrush fiasco are treated with "decency and fairness" as he arrived at the Home Office to take up his new job.
The former investment banker was given the job during a telephone call with Mrs May and becomes the first person from an ethnic minority background to hold one of the four great offices of state.
He said: "The most urgent task I have is to help those British citizens that came from the Caribbean, the so-called Windrush generation, and make sure that they are treated with the decency and the fairness that they deserve."
He added: "We are going to have a strategy in place that does something the previous home secretary set out last week when she made a statement to Parliament about making sure we have an immigration policy that is fair, it treats people with respect and with decency.
"That will be one of my most urgent tasks, to make sure we look carefully at the policy and make sure it achieves just that."
He was replaced as Secretary of State for Housing, Communities and Local Government by former Northern Ireland secretary James Brokenshire, who has recently returned to Westminster after treatment for cancer.
International Development Secretary Penny Mordaunt takes on Ms Rudd's former responsibilities as Minister for Women and Equalities.
Mr Javid's appointment was welcomed by Cabinet colleagues.
Culture Secretary Matt Hancock hailed him as "a serious political thinker who gets things done" while Chief Secretary to the Treasury Liz Truss described him as "effective, no-nonsense and brave".