Arriving for an EU Council summit to sign off an extension to Article 50, the Prime Minister was asked if she would lead the UK out of the EU without a deal and said the most important thing was for parliament to deliver on the result of the referendum.
Brussels is insisting that any delay to Brexit is condition on parliament approving Mrs May's deal, and that the extension only runs to the date of European elections on 23 May, not the Prime Minister's requested date of 30 June.
"So far as we're concerned, we think there's an urgency in constructing a majority for an agreeable solution and that's what we're concentrating on at the moment," he said.
"We think that what we are proposing can be achieved in the British parliament. We do believe we can construct a majority which will prevent the crashing out and all the chaos that will come from crashing out, and that is what we are absolutely focused on."
Mr Corbyn added: "We are therefore looking for alternatives and building a majority in Parliament that can agree on a future constructive economic relationship with the European Union.
Accompanied by shadow Brexit secretary Sir Keir Starmer, Mr Corbyn said: "This morning's meetings have been positive and we have done what I believe the Government ought to be doing - instead of bringing back a twice-rejected deal to the British Parliament, looking for constructive solutions.
"We've been discussing how this could come about and trying to reach out here as both Keir and myself have been reaching out to colleagues in all parties in the UK Parliament."
EU leaders will hold four hours of talks on Thursday afternoon following a fifteen minute presentation from Mrs May. She is expected to join fellow leaders for dinner and stay in Brussels overnight.
Speaking on arrival, the Prime Minister said: "What is important is that parliament delivers on the result of the referendum and that we deliver Brexit for the British people.
"I sincerely hope that we can do that with a deal, I am working on ensuring that parliament can agree a deal so that we can leave in an orderly way.
"What matters is that we deliver on the vote of the British people. What matters is that we recognise that Brexit is the decision of the British people. We need to deliver on that.
"We're nearly three years on from the original vote. It is now time for parliament to decide."
The statement, seen to be pitting the public against parliament, was described as a "low blow" by one former Tory minister.
No 10 defended her comments, saying they had been intended as a "message to the public" to explain why she had decided to seek an extension to the Article 50 withdrawal process.