Shadow health secretary Jon Ashworth has said there is "no appetite" for a second referendum on Brexit.
The shadow cabinet minister added that there was no consensus on a course of action he and other Labour frontbenchers have mooted in the past.
Mr Ashworth also backed comments from Labour deputy leader Tom Watson that Jeremy Corbyn was completely secure in his position and would not face fresh challenges to his leadership.
It comes after Labour splits re-emerged on Brexit in Parliament, with nearly 50 of its MPs defying the party whip to support an amendment calling on the UK to stay in the European single market.
Appearing on The Andrew Marr Show on BBC One, Mr Ashworth was asked about holding a second referendum on the EU.
He said: "I have mooted that in the past, but I don't think that is a position that has broad consensus any more.
"That was something I speculated about in discussions such as this in an interview once, but clearly there's no appetite for that, not that I can sense anyway."
Labour has performed strongly in polls following last month's general election, with a Opinium survey for the Observer putting the party at 45%, compared with 39% for the Tories, while a poll by Survation had the Tories on 41% and Labour at 40%.
In the June 8 general election, Labour also got 40% of the vote.
Mr Watson told the Observer: "I think everyone knows now Jeremy's position is completely secure as leader.
"He has had a unified PLP (parliamentary Labour party) around him since his second election win, more or less, and now he has got a highly enthused PLP around him, to take him through the years ahead."
Mr Ashworth backed Mr Watson's comments, but appeared to distance himself from comments by party chairman Ian Lavery that Labour was "too broad a church" as a party.
This was seen by many as a warning to Labour moderates who fail to support Mr Corbyn's bid to move the party to the left.
Mr Ashworth told Marr that Labour had always been a broad church and had different opinions "but we should remember that we are a united party now".
He added: "I suspect the point Ian Lavery is making is that Jeremy is now secure as leader of the Labour Party.
"Nobody is going to be challenging Jeremy, we're not going to have the turmoil we've seen in recent years.
"The turmoil in British politics is now in the Conservative Party."
Mr Ashworth defended the party's split on Brexit on Wednesday, on an amendment tabled by Labour MP Chuka Umunna, saying Labour had consistently pledged to put jobs and prosperity first and retain the benefits of the single market.
"We shouldn't get swept away in all the sort of constitutional arrangements about what that necessarily looks like," Mr Ashworth said.
Labour MP Stella Creasy, who was among the Labour MPs to back Mr Umunna's amendment, told Marr: "What a lot of us are saying is we want, in these negotiations, all options to be on the table.
"To have a Government that has forced through a hard Brexit, especially in light of the General Election result, where the public very clearly rejected Theresa May's approach, doesn't make sense to us."
She added: "What we do know is if you walk in the room and you throw away something like single market membership - 650,000 jobs in London alone are part of that - it's irresponsible."
Mr Umunna's amendment also called for Britain to stay in the EU customs union and shadow justice secretary Richard Burgon, an ally of Mr Corbyn, gave another hint that Labour could support staying in the tariff-free bloc.
The Government has committed to leaving the customs union to gain the freedom to strike free trade deals with other countries.
But Mr Burgon told BBC Sunday Politics: "I think we need to leave all the options open on that and we need to negotiate without putting options off the table.
"British manufacturers gain a lot and their workers therefore do as well in terms of jobs from the current arrangement in terms of the customs union so what we want is an equivalent benefit.
"So we want the benefits of being in the customs union even if when we leave the European Union, we can't be in the customs union."
Shadow Northern Ireland secretary Owen Smith, who has backed holding a second EU referendum, told Sky's Sophy Ridge on Sunday he still believed Brexit was "a bad decision".
He added that he believed it would be shown the Government could not deliver on its promise to retain the benefits of the single market and customs union.
"At that point, I think the country may well find itself looking down the barrel of a Brexit that is going to leave us worse off, and some of the arguments that some of us have made in the past and will continue to make in the Labour Party respectfully with our colleagues may well feel a bit more relevant then," said Mr Smith.