Nor was it clear what kind of second referendum Corbyn supports. Brexit opponents want voters to be given a clear choice of leaving or staying in the European Union.
Others say a second referendum, if it ever took place, should be more limited - asking voters, for example, if they support the deal May has negotiated with the European Union or not.
This week will see MPs in Parliament likely putting forward motions seeking to delay Brexit beyond the scheduled departure date of March 29. Other amendments will try to stop Britain from leaving the European Union with no deal - a scenario that could cause economic chaos.
Corbyn said that Labour would also introduce its own amendment, laying out Labour's alternative deal for much softer Brexit that May has negotiated with the Europeans, which would keep Britain in an EU customs regime and single market. Such an arrangement would likely mean that Britain would have to continue to accept the free flow of immigrants from Europe.
Corbyn said that only if Parliament - and the Government - rejects Labour's vision for Brexit would he and his party rally around a second referendum in order to stop May's deal.
May spent the weekend in the Egyptian resort of Sharm el-Sheikh, at a meeting of the leaders of Europe and Arab states, seeking support for additional language to her Brexit deal that would make it palatable to her own party.
Many Conservative Party MPs have rejected May's Brexit deal because it could keep Britain too closely tied to Europe in order to guarantee that there be no return of a hard border in Ireland.
While in Egypt, British Prime Minister resisted calls to seek a delay for Brexit.
"A delay in this process doesn't deliver a decision in Parliament and it doesn't deliver a deal," she said at a news conference. "What it does is precisely what the word delay says, it just delays the point in which we come to that decision."
Corbyn's spokesman said the Labour leader believes May is "recklessly running down the clock" in an attempt to "force MPs to choose between her botched deal and a disastrous no-deal".
Corbyn's move toward backing a second referendum was applauded by Labour leaders who don't like Brexit.
David Lammy, a Labour MP who backs a second referendum, tweeted, "This is a big step towards uniting our party and most importantly our country. No Brexit deal meets the fantasy promised in 2016. So the only way any specific form of Brexit can be made legitimate is through ratification in a #PeopleVote which includes the option to remain."
London Mayor Sadiq Khan said a second referendum would be "the right decision for London - and for the whole country - to give the public their say for the first time on a final Brexit deal. I hope members of Parliament will support this move, which is vital to protect jobs and growth. The Prime Minister must now withdraw article 50 to prevent Britain crashing out of the EU without a deal within weeks and to give us time to sort out her mess."
