The shadow home secretary Yvette Cooper has said reform is needed to ensure that Britain has "properly managed migration.
During a speech at the Institute for Public Policy Research, Mrs Cooper denied that for Labour to discuss immigration "is a move to the right"
Instead she insisted that a "serious debate" is needed to ensure that it is "properly controlled".
"As Ed Miliband has said a One Nation immigration policy needs to work for all. That means an honest and open debate. It means admitting where we got things wrong and changing.
"It is because immigration is so important for Britain’s future that we need a fair, controlled system that people can support", she concluded.
More top news
At least 20 people have been wounded by a car bombing outside an Istanbul football stadium, just two hours after a match ended.
Syrian government forces are continuing a push for total control of Aleppo, while a reported 20,000 civilians left the city on Saturday.
Rex Tillerson is president of Exxon Mobil and has close business links to Russian President Vladimir Putin.