Liz Kendall, the Labour leadership contender, has suggested she could back a benefits curb on EU migrants, saying removing tax credits available to them is "definitely something we should look at".
But the shadow health minister told BBC 1's The Andrew Marr Show that there needed to be a wider debate on the issue.
"We do have to deal with the issue of people who come here to work. They must be working and not claiming benefits," she said.
Asked if she was in favour of a proposal to remove tax credits to migrant workers, she replied: "That's definitely something we should look at, but this is a far bigger debate."
When pushed further on the issue, she said: "I'm in favour of free movement of labour but not free movement of benefits. People who come here should come here to work."
She criticised Prime Minister David Cameron for putting "internal political management" before the national interest, saying he had reduced the question of the UK's future relationship with the EU to the issue of migration.
Labour is split over how strongly it should campaign in favour of Britain remaining in the EU.
Andy Burnham, a rival to Kendall for the Labour leadership, has said that he would mount a Labour campaign to remain a part of the EU that would run separate from the Conservative's own Yes campaign.
Many in Labour believe the party's disastrous election results in Scotland in May's general election was due partly to their party joining forces with the Conservatives in the Better Together campaign.
(Additional reporting by agencies)Reuse content