He said the Falkland Islanders should "of course have an enormous say" over their future, but not an absolute veto.
Speaking to the BBC's Andrew Marr show, he said: "I want to play a full part in the nuclear non-proliferation treaty.
"If anybody uses a nuclear weapon, it is catastrophic for the whole world. Greater security in the world is not found through nuclear weapons".
John McDonnell, the shadow chancellor, told the BBC this morning that jobs in the nuclear industry will be "guaranteed" if Trident is scrapped.
Mr Corbyn also told the BBC he believed that workers should be able to strike in "sympathy" with workers from other industries and he would repeal the current law.
"Sympathy action is legal in most other countries and I think it should be legal here", he said.
Responding to Mr Corbyn 'sympathy action' comments, Len McCluskey, the Unite union leader, told Radio 5 Live's Pienaar's Politics: "What I’ve seen is a Labour leader on the side of ordinary working people".
He said that Mr Corbyn's support for sympathy strikes was "absolutely first class" and said it would be "sensible to give a free vote" to Labour MPs on renewing Trident.
Asked by the Andrew Marr show to respond to the suggestion from Mr McCluskey that Mr Corbyn has three years to prove himself as the Party's leader, he said: "I'm doing my best to try to ensure we change the terms of debate in Britain about the kind of society we want to live in".
When asked by Radio 5 Live's Pienaar's Politics if Labour MPs will get a free vote on Trident, Mr McDonnell said: "That will be part of the discussions that we have and the consultation that will take place."
Challenged on whether he was in favour of a free vote, he replied: "Not necessarily, I don't want to pre-empt the consultation that's taking place.
"Don't mistake democracy for division. Dissent will not be pounced upon. In some instances, we'll make sure dissent is accommodated."
Source: http://telegraph.feedsportal.com/c/32726/f/579309/s/4cebc21c/sc/13/l/0L0Stelegraph0O0Cnews0Cpolitics0CJeremy0ICorbyn0C1210A40A790CJeremy0ECorbyn0Esays0Ehe0Ewould0Ekeep0Esubmarines0Epatrolling0Ethe0Eworld0Ewithout0Eany0Enuclear0Eweapons0Bhtml/story01.htm