And shadow home secretary Diane Abbott is happy for EU migration to remain at current levels after Britain leaves the bloc.
Labour deputy leader Tom Watson would not rule out a second vote but Ms Abbott insisted “the Labour Party doesn’t support a second referendum and we’ve never supported it and don’t now”.
Mr Watson said: “We’ve not said we want a second referendum. What we actually want is a negotiated settlement.”
But, pushed to rule out a rerun, he said: “When you’re in complex negotiations on behalf of the nation you shouldn’t rule anything out.”
Shadow international trade secretary Barry Gardiner said Labour “has not said that we will have a second referendum”, and shadow justice secretary Richard Burgon said the party “isn’t arguing for” one.
Ms Abbott refused to commit Labour to seek to cut numbers from the EU, agreeing “free movement” would end when Britain left.
But businesses and public services feared they would be in a “terrible position” if EU migration “collapsed”.
“Business, the CBI, the Institute of Directors, health, education and social care – they say they need these European migrants and we have to listen to them,” she told Andrew Marr on BBC One.
Labour was currently discussing a migration system of “fair rules and reasonable management” but she repeatedly refused to say that reduced numbers should be a goal.
Mr Burgon told BBC One’s Sunday Politics that Labour was “open-minded” about whether the European Court of Justice should have power over the UK after the initial transition period planned to smooth exit after Brexit day in March 2019.
Immigration Minister Brandon Lewis said: “Today confirmed Labour’s Brexit approach is a shambles.
“They won’t rule out a second referendum and can’t say what their policy is on immigration or continuing to pay into the EU.”