Labour members have voted in favour of a £15 per hour minimum wage amid a row over the policy at its conference.
The vote is not binding, but comes after MP Andy McDonald resigned from shadow cabinet, saying he had been ordered to argue against the rise.
The leadership did not encourage members to back or reject the motion.
But earlier, Sir Keir Starmer told Sky News he stood by the party’s current policy of raising the minimum wage to “at least” £10 an hour.
Left-wingers – including former leader Jeremy Corbyn – had called on Sir Keir to back to larger rise.
Mr Corbyn told the BBC it was something the party “should be supporting and campaigning for”.
Arguments between the left, including supporters of Mr Corbyn, and Labour members loyal to Sir Keir have dominated the party conference in Brighton.
Sir Keir pushed through reforms to the party election rules, seen as unfavourable to left-wing members of Labour, in a vote on Sunday.
The Unite union put forward a motion calling for the minimum wage to increase to £15 to a vote on Tuesday.
The current minimum wage is £8.91 for those 23 and over, £8.36 for those aged 21 and 22, and £6.56 for 18 to 20-year olds.
The wide-ranging Unite motion also said that, for Labour to win the next election, it “must be an anti-austerity party, defending jobs and improving living standards”.
And it included demands for stronger union rights, higher taxes “on the very wealthiest”, an end to zero-hour contracts and a “better work-life balance”.
But asked about the wage rise earlier, Sir Keir said: “It should be a £10 minimum wage – that’s a 12% increase [meaning] £2000 a year for working families.”
Before the vote, shadow home secretary Nick Thomas-Symonds said the party leadership was “perfectly happy” for conference delegates to back the £15 motion.
However, he said Labour would only reassess its current policy closer to the next general election, adding this was the “responsible thing to do”.
But Mr Corbyn called for the party to commit to a £6 an hour rise in the minimum wage now.
Speaking at a fringe event alongside Labour’s conference, the former leader told the BBC: “We live in a low-wage economy and a low-wage economy leads to poverty. We live in a society now with more food banks than branches of McDonald’s. That’s where we have got to.”
Mr Corbyn also praised Mr McDonald, saying he had “huge admiration” for the MP, adding: “He went through a lot of trauma [on Monday] because he did not in all conscience feel he could go and say that he was opposed to £15 minimum wage because he is not.
“He supports it, so he took the decision he did to resign. I fully support him.”
Raising the minimum wage was not one of the 10 pledges Sir Keir made when running for the Labour leadership last year.
But he supported a campaign in 2019 for fast food chain McDonald’s to improve pay and conditions.
At the time, he said: “They’re not asking for the Earth. They’re asking for the basics – £15 an hour, the right to know their hours in advance and to have trade union recognition. That ought to be the norm in 21st Century Britain.”
But on Tuesday, Sir Keir said his comments were in relation to “particular industrial disputes at McDonald’s”, adding: “I backed them in that and I’d back them again today in relation to that the minimum wage, [but] across the whole of the economy is a completely different issue.”
In a scathing resignation letter, Mr McDonald claimed the leader’s office had instructed him go to a meeting at the party conference and “argue against a national minimum wage of £15 an hour and against statutory sick pay at the living wage”.
“After many months of a pandemic when we made commitments to stand by key workers, I cannot now look those same workers in the eye and tell them they are not worth a wage that is enough to live on, or that they don’t deserve security when they are ill,” the former shadow employment secretary added.
Mr Corbyn also backed the so-called “McStrike” in 2019, but his policy as leader was for at least £10 minimum wage – also Labour’s current position.