Antonio Tajani, the European Parliament President, said: "I listened carefully to what May had to say".
The SNP's Stephen Gethins said it was clear the PM had "failed to bring forward any meaningful proposals to end the deadlock created by her Government".
Speaking to the BBC on Thursday, the prime minister said she hoped that no extension would be needed but acknowledged that it may be necessary to lengthen the transition period by a "matter of months". "We should not call a summit just to talk", the Taoiseach said.
The Labour leader went on to issue caution, warning that instead of "using Brexit to rebuild Britain", the government will "slash rights and protections and turbocharge their bankers-first market free-for-all".
"And what Michel Barnier has indicated very clearly is that the European Union side, certainly, is willing to allow more time in the transition period to agree an alternative solution to a backstop".
"If Theresa May is asking for a longer transition period, she is stalling", Dorries tweeted.
"Both sides mentioned the idea of an extension of the transition period as one possibility which is on the table and would have to be looked into", he added.
A spokesperson for the prime minister refused to categorically rule out an extended transition period earlier on Wednesday, telling reporters in Westminster: "We're not calling for an extension to the implementation deal".
"We want a Brexit that is good for the union in all of its constituent parts, but that also respects the constitutional and economic integrity of Northern Ireland", she added.
Most EU leaders struck a note of cautious optimism that a deal would eventually be reached even though there was disappointment that, as expected, May offered no new proposals on how to break the impasse. "That would backfire spectacularly".
The 27 heads of government also listened to European Union commission president Jean-Claude Juncker's presentation on preparations for a no-deal scenario.
His comments come in the wake of statements made by US Commodity Futures Trading Commission (CFTC) chair Christopher Giancarlo, who threatened to prevent European banks from accessing US futures markets over EU plans for the oversight of foreign clearing houses after Brexit.
He conceded "we are not so far" from a deal but cautioned that "now we must accelerate the work".
"I believe a deal is achievable and now is the time to make it happen", the prime minister told journalists at the EU Council meeting on Wednesday. By the end of the day, a November summit that had been planned to move into the next phase of discussions had been called off, due to a lack of progress. "They were taking credit for the amendments to the Joint Report last December and now it is coming back to bite us all". Others at the bar managed to capture videos of the four leaders enjoying themselves and, naturally, posted them online. "It is a problem", she declared. "Please, it's a wonderful evening", she replied. "There is still time for the drama to play". Paris suggested Britons would need visas to travel to France in the event of a no-deal. Otherwise it is a no-deal Brexit.
"Now the key element for a final deal is on the British side".
Lara Spirit, Co-President of anti-Brexit youth campaign group Our Future, Our Choice said the polling indicated "widespread dissatisfaction with the omnishambles of this Brexit process". If it was not passed, any amendments would be regarded as merely "points of view".
Business Insider reported last week that Leadsom, Mordaunt and Work and Pensions Secretary Esther McVey were all prepared to quit Cabinet if the prime minister did not change her plans for the Brexit backstop.
The possibility of an extension has infuriated hard-Brexit backers in Ms.
"Can the Prime Minister confirm what action the Government is taking to ensure this important sector for our economy continues to be able to access the workforce it will need?"