Mr Corbyn said his “priority” was to work towards blocking a no-deal Brexit, with an election afterwards.
But Mr Blair warned Labour could “struggle” at any poll held before the Brexit issue was “resolved”.
The ex-PM said some voters “may fear a Corbyn premiership more” than a no-deal scenario.
At a speech in Salford, Mr Corbyn said an election was the “democratic way forward” and “would give the people a choice between two very different directions”.
The BBC understands “live discussions” are going on in No 10 about asking Parliament to approve a snap poll if MPs wanting to block a no-deal Brexit defeat the government this week.
Under the Fixed Term Parliament Act, the prime minister could call a general election if two-thirds of MPs vote for one.
One could also be held if a motion of no confidence was passed and no alternative government was confirmed within 14 days.
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The prime minister has said he wants the UK to leave the EU on 31 October, with or without a deal.
However, a number of MPs from his own party, as well as the opposition, are against a no-deal Brexit and are expected to bring forward legislation on Tuesday to try to block such a move.
Mr Corbyn said his first priority was to “bring the country back from the brink” and do everything possible to prevent no deal, before then pushing for an election.
“When a government finds itself without a majority the solution is not to undermine democracy,” he said.
“The solution is to let the people decide and call a general election.
“It is the people not an unelected prime minister who should determine our country’s future.”
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Shadow Brexit minister Jenny Chapman also said she would welcome an election, but added that “stopping a no deal must come first”.
However, former Labour leader Tony Blair warned that whilst an election would be necessary after Brexit is “resolved”, the party could struggle if the vote is held beforehand.
He said Labour should vote against holding an election if the government seeks to have one now.
“Boris Johnson knows that if no-deal Brexit stands on its own as a proposition, it might well fail,” he said.
“But if he mixes up the Brexit question with the Corbyn question in a general election, he could succeed, despite a majority being against a no-deal Brexit, because some may fear a Corbyn premiership more.
“He [Mr Corbyn] should see an election before Brexit is decided, for the elephant trap it is.”
Labour politicians would have very, very different views on whether to support the PM if he called for an election.
One source said Labour couldn’t allow itself to be in a situation where we have an election and we leave the EU during that election.
But Mr Corbyn did seem to indicate he would back going to the polls.
It would be rather awkward for him not to, when he and senior Labour politicians have been calling for a general election for such a long time.
It is interesting to note that in 2017, when the same quandary was put to Labour, some argued they should not support Theresa May’s call for a general election.
But in the end, some accounts say Mr Corbyn felt allowing people to have a vote was much more important than anything else.
What is Labour’s position on Brexit?
The Labour leader has been urged by members of his own party to fully support the UK remaining in the EU.
Some of his closest allies, including shadow chancellor John McDonnell, have already done so.
Mr Corbyn’s position is that he wants a general election, which would see Labour argue for a public vote on the terms of leaving the EU, with Remain on the ballot paper.
When asked how the party would campaign in such a vote, Mr Corbyn said it would depend on the other option.
“If it is no deal, we would vote for Remain,” he said, but added that if there was another deal on offer “the party’s democratic processes will decide”.