Corbyn has so far been equivocal about his support for a second referendum. If he does throw his weight behind another ballot - which is still to be confirmed - it could be decisive. About 10 Conservative MPs are already campaigning for another plebiscite.
Two years since the first referendum, the UK has yet to negotiate an exit accord that can win the backing of Parliament. May's deal was rejected by MPs last week by a historic margin and she is now trying to revise the agreement with the EU to win over opponents at home.
"Our amendment will allow MPs to vote on options to end this Brexit deadlock and prevent the chaos of a No Deal," Corbyn said. "It's time for Labour's alternative plan to take centre stage, while keeping all options on the table, including the option of a public vote."
The amendment does not commit the leadership to actually backing such a vote were it to take place. The formula of "keeping all options on the table" echoes a compromise deal agreed by the party last year that has enabled Corbyn, a lifelong Eurosceptic, to hold off demands from rank-and-file members and MPs to support a second referendum.
"This is a huge step forward and shows the Labour leadership's commitment to stop a disastrous no deal exit," said Mike Buckley, director of Labour for a People's Vote. "We still need clarity on Labour's position in a public vote and whether, as members want, we would campaign robustly for our continued membership of the EU."
May rejected calls for a second referendum from MPs on all sides during an appearance in the House of Commons yesterday. Warning it would "damage social cohesion by undermining faith in democracy," she said it would break the trust of the voters who backed leaving the EU. May said she doesn't believe there's a majority for a referendum in the House of Commons.
The Labour move might play into May's hands. Pro-Brexit hardliners in her party could decide that the deal she negotiated is a better option than risking a re-run of the referendum that could reverse the decision of 2016. Some in Labour's ranks are also uncomfortable with the prospect of asking voters again.
Tusk told Cameron, vote 'stupid'
Donald Tusk warned David Cameron he would "lose everything" if he went ahead with his "stupid referendum" - but the British Prime Minister told his EU counterpart not to worry.
Tusk, the president of the European Council, said he told Cameron to "get real" when the latter tried to negotiate a better relationship with the bloc ahead of the 2016 referendum. Tusk said when he warned Cameron about the scale of the challenge he was facing in trying to persuade EU leaders to sign off on membership reform for the UK "for the first time I saw something close to fear in his eyes".
The remarks were made by Tusk in a new BBC series called Inside Europe: Ten Years of Turmoil.
Tusk said Cameron was confident the referendum would not go ahead because he believed he would be part of a coalition after the 2015 election and the Liberal Democrats would block it. "But then, surprisingly, he won and there was no coalition ... Cameron became the real victim of his own victory."
- Telegraph Group Ltd, Bloomberg