May's abrupt move less than 30 hours before parliament was to vote opens up a range of possibilities from a Brexit without a deal, a last-minute agreement or another European Union referendum, the news agency said.
EU leaders have insisted that the backstop can not be taken out of the deal, but May is sure to seek flexibility on this from her European partners.
May is expected to face a leadership battle over the House of Commons' vote on the Brexit deal, as 48 no-confidence letters against May from members of her ruling Conservative Party could prompt her defeat, Sputnik previously reported.
He said: 'The government is in disarray, uncertainty is building, uncertainty is building for business, people are in despair at the state of these failed negotiations and concerned about what it means for their jobs and communities - and the fault of that lies exclusively at the door of this shambolic government'.
A spokesman for Tusk said the timing of the meeting, which will come on the first day of a planned European Council summit, was still to be determined.
The backstop would see the entire United Kingdom kept within a customs union with the EU for an indefinite period of time, which Brexiteers argue could trap Britain into abiding by EU rules and making financial contributions forever.
May plans to travel to Dublin on Wednesday to continue her whirlwind tour to rescue her Brexit deal.
However, Irish Prime Minister Leo Varadkar said it was not possible to renegotiate the Irish border backstop proposal without "opening up all aspects" of the Brexit withdrawal agreement.
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"It's been evident for weeks that the Prime Minister's deal did not have confidence of this House yet she plowed on regardless, reiterating "this is the only deal available", Corbyn said.
Mrs May told the Dutch PM that "additional assurances" would be needed on the backstop arrangement to keep the Irish border open after Brexit if the deal was to get through Parliament.
British Prime Minister Theresa May (L) and European commission President Jean-Claude Juncker (R) prior to a meeting in Brussels. "Everyone has to know that the Withdrawal Agreement will not be reopened".
"For as long as we fail to agree a deal, the risk of an accidental no deal increases", she told MPs.
"We are now actively, not only preparing for that, but taking actions to ensure that if necessary we will be ready on March 29 for Britain to leave the European Union without a deal", Mr Coveney told Irish national broadcaster RTE, adding that he still thought a no-deal Brexit was unlikely.
"I imagine they'll add some language saying that both sides remain convinced that we'll never need to use the backstop", he told AFP.
"The government has lost control of events and is in complete disarray", said opposition leader Jeremy Corbyn.
May said the broader question was whether parliament wanted to deliver on the will of the people for Brexit, or open up the divisions in the world's fifth largest economy with another referendum.
He added: "I have no difficulty with statements that clarify what's in the withdrawal agreement but no statement of clarification can contradict what's in the withdrawal agreement".