After two senior Labour figures - Margaret Hodge and Ann Coffey - tabled a motion of no confidence in the leader, Corbyn said he was aware of unrest within the party but would not buckle to the calls for him to resign.
"Yes there are some people in the parliamentary party who would probably want someone else, they've made that abundantly clear," Corbyn said.
Asked specifically whether he would keep his name on the ballot in any leadership contest that made it to the vote of Labour party members, Corbyn said: "Yes, I am here."
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Since Labour party members, who overwhelmingly backed the Islington MP in last year's contest, have the final say over the party leader, Corbyn is likely to win any tussle in which they are given a say.
In the speech in London this morning, Corbyn also expressed regret at the result of the EU referendum and acknowledged concerns in the country over immigration were legitimate.
He added shadow home secretary Andy Burnham - who is running to become mayor of the new Greater Manchester region - will be looking at the issue, and outlined Labour's support for establishing a "migration impact fund" to direct money towards areas of the country where migration adversely affects public services.
Corbyn then went on to attack companies that bring in low-paid workers from overseas, use zero hours contracts and undercut the wages of British citizens.
He also dismissed calls for the UK to hold a second referendum on EU membership as he called on the Labour Party to be given a big role to play in the upcoming negotiations over the terms of the UK's exit.