In a statement from Downing Street, Mrs May said she wanted to agree a new plan with Mr Corbyn and put it to a vote in the Commons before 10 April - when the EU will hold an emergency summit on Brexit.
If she and Mr Corbyn do not agree a single way forward, she proposed putting a number of options to MPs "to determine which course to pursue".
The PM said she understood some people were "so fed up with delay and endless arguments" they would prefer to leave without a deal, and she believed the UK "could make a success of no-deal in the long term".
But she added that leaving with a deal was "the best solution".
"This is a difficult time for everyone," said Mrs May. "Passions are running high on all sides of the argument, but we can and must find the compromises that will deliver what the British people voted for.
"This is a decisive moment in the story of these islands and it requires national unity to deliver the national interest."
How has Brexit unfolded?
November 2018: UK agrees withdrawal agreement and framework of future relations with EU
December 2018: Theresa May postpones first meaningful vote on deal to seek further assurances from EU
15 January: House of Commons rejects overall Brexit deal by 230 votes
13 March: MPs vote down Brexit deal for second time by 149 votes
22 March: EU agrees to delay Brexit beyond 29 March - but only to 12 April if UK can't agree deal within a week
29 March: MPs reject withdrawal agreement on its own by 58 votes
2 April: PM says she will seek further "short extension" from the EU
Labour MP Lloyd Russell-Moyle said his party leader only found out what the statement contained when it was shown on TV.
He told BBC Radio 5 Live's Drive programme that he was next to Mr Corbyn as he watched in silence - before the leader left the room to prepare a response. Mr Russell-Moyle said the feeling was "this is all a bit late".
After the statement, president of the European Council, Donald Tusk, called for patience.
Even if, after today, we don’t know what the end result will be, let us be patient. #Brexit