Isle of Wight Labour voted overwhelmingly to support Mr Corbyn in last year's leadership contest, and at their recent AGM members voted 45 to 16 with some abstentions to reaffirm support for Mr Corbyn and to call on the Parliamentary Labour Party to halt the leadership contest.
But Mr Smith has the nominations of 162 of the party's MPs - some 70% of its representation in the Commons - along with half of Labour's MEPs.
Jeremy Corbyn has told Sky News that he is not a bully following allegations from senior Labour MPs Connor McGinn and Angela Eagle.
Answering questions following a speech in London, Mr Corbyn said: "I say to Labour MPs quite simply this - I've been in Parliament a very long time".
"If we say we are going to start restricting then it works both ways, it will also restrict British people going to live and work in Europe".
"Over the coming weeks, I look forward to listening and speaking to as many members and supporters as possible, to set out my radical vision for Labour's future".
McGinn said he chose to speak out after watching an interview Corbyn gave to the BBC's Newsnight on Thursday. I know they will have got involved for the same reasons I did, because they want to tackle inequality and be part of building a fairer Britain and world.
Corbyn's comments will serve as a warning to Labour rebels who will face a clear choice between backing the socialist leader or the moderate Labour MP Owen Smith.
But Corbyn insisted he had delivered real results since taking control, saying that his Labour opposition had killed off the government's austerity-led economic approach. I am joining again and stating that I am joining to support the Labour Party so that they don't block my membership.
The local branch of the Union of Construction, Allied Trades and Technicians (UCATT) branded the challenge to Mr Corbyn's leadership as a "coup" and condemned St Helens North MP Conor McGinn's support for challenger Owen Smith.
Ms Eagle said a "permissive" environment had been allowed to develop in which MPs opposed to Mr Corbyn faced abuse.
A party official said that the total number is likely to change as Labour goes through its applicant checking "political vetting" process.
"I am very surprised and actually very disappointed they should say that". It previously emerged that she joined the Labour Party just before being given the task. I have had threats too and I am telling him "it has got to be stamped out and we have to have zero tolerance" of this in the Labour Party.
Corbyn is now the bookies favourite, with bookmakers offering odds of 11/2 for him to win while the odds for rival Owen Smith are marked up at 25/2.
"Today, we are more than 45 years on from the Equal Pay Act, 40 years on from when I was chasing down lost pay for women workers and still, still, women are paid 20 per cent less than men."