MPs have just voted by 286 to 344 to reject the government's withdrawal agreement on the day the UK was due to leave the EU.
Theresa May said it is a "matter of profound regret that once again this House been unable to support leaving European Union in an orderly way".
Several Brexit-backing Conservative backbenchers who had rejected the deal in the first two meaningful votes, including the former Brexit secretary Dominic Raab, switched sides during the debate, to support the agreement.
But with Labour unwilling to change its position, and the Democratic Unionist party's 10 MPs determined not to support it, it was not enough to secure a majority for the prime minister.
The prime minister added the "implications are grave". "The default is the UK due to leave on 12 April - in just 14 days time."
May said any way forward is "almost certain to involve UK being required to hold European Parliamentary elections".
She added: "I fear we are reaching the limits of this process in the House."
Jeremy Corbyn accused May of offering Britain a "half-baked Brexit" which Labour could not support.
The vote was held on the day when Britain was meant to be leaving the European Union.
The European Council announced the special gathering of EU leaders within minutes of the Prime Minister's defeat in the House of Commons. Writing on Twitter, Tusk said: "In view of the rejection of the withdrawal agreement by the House of Commons, I have decided to call a European Council on April 10."
MPs are due to hold another series of "indicative votes" on Monday, a process initiated by a cross-party group of backbenchers led by Oliver Letwin, in a bid to find a majority in the House of Commons for some way out of the impasse.