Yvette Cooper has condemned Theresa May for suggesting EU citizens working in Britain might have to leave after Brexit.
The former shadow home secretary said May, who is most likely to succeed David Cameron as prime minister, should stop "nasty go home" campaigns that had sprung up since last week's result.
May told ITV's Peston On Sunday that the status of EU nationals living in Britain - and Britons living in the EU - would remain the same until negotiations were concluded, which could take years.
When asked if they could stay here forever, she said: "Well, nobody necessarily stays anywhere forever."
After the interview, Cooper tweeted:
She added: "People from across the political spectrum, including from those who campaigned for Britain to leave the EU, have called on the government to guarantee their status before the summer recess.
"Doing so would help with the urgent task of bringing our country back together and help to stamp out the nasty repatriation campaigns which do not represent our country.
"Parliament can choose to do this without waiting for the negotiations. The Home Secretary could accelerate this - she has a responsibility to do this right now while she is in her current job, rather than just spending her time campaigning for her next one.
"In the interests of community cohesion, the Prime Minister should get it sorted out right now."
It comes after Cooper was among the signatories to an open letter that called for immediate guarantees that EU Citizens would not be deported.
Both Leave and Remain campaigners signed the letter.
May's comments on Peston On Sunday led people to point out the anguish and insecurity this would mean for the three million EU nationals who live here.
On Peston On Sunday, May said: "At the moment we are still a member of the EU and the arrangements still continue, so there is no change to their position currently but, of course, as part of the negotiations we will need to look at this question of people who are here in the UK from the EU.
“I want to ensure that we are able to not just guarantee a position for those people, but guarantee a position for British citizens who are over in other member states, in other countries in Europe, and living there.”
Andy Burnham, the current shadow home secretary and former leadership candidate, said May's leadership rival Michael Gove was a "better politician and person," adding he hoped Gove would be prime minister instead of her.