Labour has suggested it could back a Conservative cap on immigration from outside the UK.
The surprise move came as leader Ed Miliband called on the UK to work harder to integrate outsiders.
Mr Miliband also apologised for what he said was his party's failure to control immigration or deal with racial and ethnic segregation when it was in power. The son of immigrants himself, Mr Miliband called for more to be done to ensure newcomers to the UK intergrated properly into society.
His set out a series of proposals including stricter English language requirements for public sector jobs.
Funding also should be channelled into English teaching ahead of non-essential translation.
Parents should be forced to pledge their children will learn English as part of agreements with their local school, he also suggested.
Also, there would be a crackdown on landlords who squeeze immigrants into overcrowded homes.
Labour would also be stricter on the use of "tied housing", where accommodation comes along with a job, which the party warns can lock migrant workers into atrocious conditions.
But in a surprise move he also signalled he was prepared to look at the idea of a cap – a policy he has previously criticised.
"We will look at how the Government's immigration cap works in practice," he said.
"But I believe we can all cope with these pressures if we recognise them and understand how to respond."
During a speech in Tooting, south London, the Labour leader also apologised for underestimating voters' concerns.
Some communities had been unable to deal with the scale and pace of immigration when Labour was in charge, he admitted.
However, PM David Cameron accused Labour of leaving the immigration system in "complete meltdown".
Figures released last month showed net immigration in the UK had fallen by one-quarter in the past year, to 183,000 in the year to March, down from 242,000 the previous year, according to the Office for National Statistics.