Asked if Jeremy Corbyn would also campaign for the United Kingdom to remain in the European Union, she said: "If it's a choice between a disastrous Tory Brexit or no deal and remaining, then that is what we will have to do".
The Labour leader, who has been a long time opponent of the European Union but has lost a number of MPs in the past week over his Brexit stance is expected to say: "The prime minister is recklessly running down the clock, in an attempt to force MPs to choose between her botched deal and a disastrous no-deal We can not and will not accept... one way or another, we will do everything in our power to prevent no deal".
"It is still within our grasp to leave the European Union with a deal on the 29th of March and that is what we are working to do", May told reporters aboard her plane, as she traveled to a summit of EU and Arab leaders in Egypt.
The party will seek to enshrine Labour's five Brexit demands in law by tabling an amendment to the Government's Brexit motion which is set to be debated on Wednesday.
The Kyle-Wilson amendment is not expected to be tabled tomorrow, but could be pushed forward on the day of the meaningful vote in March.
On Sunday, Labour's trade spokesman Barry Gardiner said that second referendum should serve as a "safety net".
After a meeting with members of his shadow Cabinet on Monday afternoon, the Labour leader finally gave way.
The Labour party will campaign to remain in the European Union if a second referendum is called, it has been announced. It is thought that refusing to support this amendment would lead to more Labour defections to The Independent Group, deepening the party split. "I think it's going to be deeply divisive", he said.
"But if we can't get that, if we can't get a deal, if we can't get our red lines met, then [party policy] is that we go for a people's vote", he said.
Voters narrowly approved the June 2016 referendum to pull Britain out of the EU.
Corbyn added that if it fails, they will instead call for a People's Vote on the final deal with the EU.
"There will be no Tory Brexit without it being a vote in the public". The question now is whether May will - either willingly or by force via the new Cooper amendment - replace her "my deal or no deal" ultimatum with a new choice: "my deal or delay Brexit, possibly for many, many months".