Jeremy Corbyn’s top team had been expected to discuss the proposals in the party’s defence review at their weekly meeting at Westminster.
However it is understood that the debate has now been referred to a future meeting.
While there was no immediate explanation for the move, it follows a warning by shadow home secretary Andy Burnham that the differences within the party on the issue may be impossible to reconcile.
The divisions within the Labour ranks were underlined when shadow defence secretary Emily Thornberry briefed MPs and peers on her thinking at a stormy meeting on Monday evening.
Afterwards, Ms Thornberry, who like Mr Corbyn favours unilateral disarmament, was branded “waffly and incoherent” by one critic. She told the Parliamentary Labour Party (PLP) meeting she wanted to carry out the ongoing review of Labour policy on Trident in an “atmosphere of mutual trust and respect”.
But in the face of hostile questions from MPs and peers, she was forced to tell them there was “no point trying to shout me down”.
Mr Burnham, who is a supporter of Trident renewal, said the meeting “confirmed something many of us had long suspected: that the debate on Trident in the Labour Party is going to be very difficult”.
He told BBC Radio 4’s Today: “There are two positions here which are difficult to reconcile - maybe impossible to reconcile - and the party has got to find some way of accommodating those positions and move forward and don’t let this issue take over everything.”
In an apparent dig at Mr Corbyn’s suggestion that a new fleet of nuclear submarines could be deployed without warheads, he said: “There are some hybrid options that have been put forward but I think most people have found that they just don’t work.So the discussion has been in the party: ‘can you realistically try to find a halfway house?’ and most people have concluded that you can’t.”
The debate comes as The Ministry of Defence announced a further £201 million support package for design work on the replacement for the Trident submarine fleets.