His comments came as the subject threatened to cause major divisions at the party conference in Brighton with Unite General Secretary Len McCluskey issuing a challenge to the new leadership over changing the policy on supporting the renewal of the UK’s nuclear deterrent.
It was claimed that the debate was axed because it failed to win enough votes in a ballot of members on topics to discuss.
In a further sign of the strength of the ill-feeling between difference factions, shadow foreign secretary Hillary Benn, a leading moderate who is in favour of replacing Trident, was removed from the party’s ruling national executive committee by Corbynites.
The new Labour leader wants the deterrent to be scrapped but accepts many in his party take the opposite view. He said there was “nothing wrong” with MPs taking a different position, hinting at a free vote next year.
The policy is due to be debated at the party’s conference in Brighton this week as part of a “people’s parliament” approach where members shape policy rather than the leader.
Mr Corbyn said he “accepts” that some of his frontbenchers “take a different view”.
But he added: “I hope to persuade them.”
However, it was clear that Mr McCluskey, the leader of the UK’s biggest union, would lead the charge against any change of policy on Trident with the backing of many in the parliamentary party.
Unite has thousands of members in the defence industry and Mr McCluskey warned that opposing the renewal of Trident would put many jobs at risk.
He said: “I understand the moral case and the huge cost of replacing Trident, especially in this era of austerity, but the most important thing for us is jobs and the defence of communities.
“We will vote against any anti-Trident motion. I don’t think this will be a problem for Jeremy Corbyn. He is a great democrat,” he said. The GMB and other leading unions are also expected to oppose any move to scrap Trident, making it virtually certain that any motion would be defeated.
Former leadership contender Chuka Umunna, who ruled out serving in the shadow cabinet because of differences with Mr Corbyn over issues including Trident, said the party would have to fix its position on such key policies.
“It’s not plausible for us as an opposition not to have a position on the defence of the realm,” he told a fringe meeting.