The motion that will be voted on by party members on Tuesday commits Labour to supporting a public vote if it can not force a general election, saying the party should consider "all options remaining on the table".
Labour leader Jeremy Corbyn and other party chiefs oppose the idea, saying Labour must honor voters' 2016 decision to leave.
He said: "We deleted a line which said that any public vote would be, "on the terms of Brexit".
Mr Corbyn told an eve-of-conference rally in Liverpool: "If this Government can't deliver, then I say to Theresa May: the best way to settle this is to have a general election".
There was a similar message from deputy Labour leader Tom Watson, who told The Observer: "Jeremy and I were elected in 2015 to give the Labour Party back to its members". It will be up to representatives of those local Labour parties to get together and put all their different motions into one "composite" motion that is acceptable to everyone.
The party said the meeting was "conducted in a cordial and respectful manner that recognised the complexities of Brexit" as agreement was sought on a motion that would instruct the leadership to first judge any deal by its six tests.
But it is not clear how far the new motion will take a party that has said for some time has said that a second referendum is not off the table.
"We believe general election is the best solution because people can then have a wide-ranging debate and also then choose the team that would then do the negotiations".
That may well win favour with well-heeled London-based members of the party, who overwhelmingly voted to stay in the bloc.
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Meanwhile, Mr Watson told the Observer there was "going to be pressure" for Labour to commit to another Brexit vote in its next election manifesto.
"We argued for Remain in the past but we lost that vote so we have to respect that", he said.
The key paragraph in the document states: "If we can not get a general election Labour must support all options remaining on the table, including campaigning for a public vote".
MPs and union leaders are expected to join a march on the opening day of the conference on Sunday to demand a so-called "People's Vote".
Bookies have slashed the odds of Theresa May winning any upcoming general election - with bookmakers.tv ranking Corbyn at 5/1 to become Prime Minister.
"We weren't ruling out options and nobody was ruling out Remain".
For those pressing for a second referendum, or a People's Vote, the motion was little more than a fudge.
Two senior members of May's Downing Street team reportedly responded to last weeks stall in negotiations on Britain's European Union exit deal by making a contingency plan to save Brexit and consolidate Theresa May's position as prime minister.
But the shadow chancellor infuriated anti-Brexit campaigners on Monday morning by echoing remarks made on Sunday by Len McCluskey, the Unite general secretary, suggesting Labour should not accept any referendum that appeared to question the result in 2016.