Yvette Cooper has called on Theresa May to "quickly" clarify the status of EU citizens currently living in the UK.
The former Shadow Home Secretary was critical of Mrs May earlier this month, after she told Peston on Sunday that EU nationals' ability to stay post Brexit would be subject to "negotiations".
Not good enough for TMay to say EU citizens already working here shd wait for negotiations to find out if can stay @pestononsunday 1/2
Speaking to ITV News, Ms Cooper said: "I do hope that she takes the opportunity very quickly to deal with the issue that she hasn't yet after the referendum, which is the fate of EU citizens who've been settled here, often for a very many years, and who still don't know whether they going to be able to stay.
"It would stop the extremists exploiting the issue, it would be a way of starting to bring people together."
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David Cameron's final cabinet meeting was marked with warm tributes, with soon-to-be prime minister Theresa May saying he has "the respect of colleagues".
But now Theresa May will decide who will make up her new cabinet.
ITV News' political correspondent Libby Wiener takes a look at the preparations for change in government.
Theresa May has called it "an honour and a privilege" to be the new Tory leader, as she thanked staff at the Conservative HQ in London.
She paid tribute to the man she will shortly replace as prime minister, saying David Cameron had been "a superb leader of our party and a superb prime minister".
She also stated that "when Labour prospers the country suffers", calling for a big win in the general election in four years time to "make sure they don't prosper".
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Theresa May and David Cameron have both exchanged tributes at a traditionally rowdy final cabinet meeting before she replaces him as Prime Minister.
The gathered Conservative ministers delivered four founds of table banging before Mr Cameron began his 215th meeting, at which the government's life chances policy and aim for Trident renewal were discussed.
Mr Cameron recounted what he believed were his cabinet's achievements since 2010 as coalition leader and upon assuming full power in 2015 and reiterated his friendship and support for Mrs May.
She responded by describing the "warmth and respect" the outgoing PM had shown to his colleagues and praised him for "always" putting the country "first" during the challenges of his administration.
Chancellor George Osborne, who is expected to be replaced in Mrs May's reshuffled cabinet, added his praise for Mr Cameron before the meeting was concluded with another louder round of table banging.
Theresa May brushed off an awkward moment outside 10 Downing Street with a shrug and a grimace for waiting photographers.
The soon-to-be prime minister emerged from what will tomorrow be her new home after the final Cabinet meeting of David Cameron's premiership and headed to a waiting car - that wasn't for her.
Realising her error, the outgoing home secretary corrected her wrong-turn and joked about the error with reporters camped on the street.
Meanwhile, a blue removals van has been spotted at the back of the famous residence to take Cameron's belongings.
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A removal van arrived at Downing Street as David Cameron held his final Cabinet meeting as prime minister.
The unmarked blue van arrived at the back of Number 10 and a man wearing a blue T-shirt featuring the words "Simply Removals" was seen speaking to a police officer at the famous address.
Cameron's successor Theresa May will take up office as Britain's second woman PM on Wednesday.