Jeremy Corbyn said he is "very honoured" to continue supporting the Campaign for Nuclear Disarmament (CND) in his new role as vice-president.
The Labour leader appeared upbeat after attending a private event with CND members at the end of the first day of the organisation's annual conference.
He said: "Thank you very much, I'm very honoured" when asked how he was feeling about his new position.
Arriving late on Saturday afternoon by black cab, Mr Corbyn wished journalists a good evening before disappearing inside to greet anti-nuclear activists.
Kate Hudson, general secretary of the Campaign for Nuclear Disarmament (CND), said she was "delighted" to welcome Mr Corbyn to the conference and could not see the "lifelong member of the CND" wavering in the face of party pressure.
She said: "I can't imagine Jeremy Corbyn changing his long-held principled beliefs. His view has been at odds with the Labour Party policy for some while clearly - I can't imagine that he would possibly change his position on that.
"It may be that he's not able to persuade in open debate the party as a whole but let's see.
"We've seen over the last decade how public opinion has shifted on Trident and we've seen military figures deciding that Trident should be scrapped ... we've seen people concerned that Britain's security needs are not met by a Cold War relic.
"We're facing things like climate change, pandemics, cyber warfare - a range of 21st century issues that are not met by Trident.
"I mean: would you nuke a terrorist for example? It's just not doing the job. Opposing Trident is the new common sense."
Conference attendees who were present for Mr Corbyn's address described a "very informal atmosphere" with groups of people singing, and said there were around 50 activists still in the room.
Peter Le Mare, from Penzance, said Mr Corbyn was asked again whether he would push the nuclear button.
He said: "He made a joke of it. He said he answered [no] like any other person would.
"He's just the same Jeremy. He sticks to his guns."
Another attendee said Mr Corbyn was "very inspirational" and that there was at least one person other than herself with tears in their eyes as he spoke.
Chair of CND Dave Webb, from Leeds, said the Labour leader was "extremely well received by everyone" at the private event.
"He doesn't seem to have changed except he's got a better haircut now. There was as much energy and enthusiasm as there's ever been.
"He spoke about his commitment to a safer world, and that we should be looking at what we mean by security - it shouldn't be based on people aggressively challenging each other."
He added it was the first time he'd seen Mr Corbyn face-to-face since his election as leader of the opposition and that "it was very good to hear him say these things in the role he's in".
The CND - which has about 35,000 members - has experienced a huge surge in popularity since Mr Corbyn's rise, with "probably two or three hundred" new members in the last week.
The organisation is planning a national demonstration opposing Trident in February next year in the run up to the parliamentary vote, Ms Hudson said.