Mr Varadkar told reporters that a regular summit had been fixed for December and clear progress would be required to show the value of a special one next month.
Nigel Dodds, the DUP's Westminster leader, dismissed the idea that extending the transition would help solve the problem of Northern Ireland.
"All of the 27 said that we wish to bring about a solution, one that clearly expresses the fact that Britain is no longer a member of the European Union, but also expresses what we all want politically speaking - namely that we establish a good relationship with Britain for the future", she told an end-of-summit news conference in Brussels.
The 27 heads of government also listened to European Union commission president Jean-Claude Juncker's presentation on preparations for a no-deal scenario. Pro-EU MP Nick Boles has said it would "madness" to extend the transition, and warned the Conservative party was now "close to despair".
Britain says it has not asked for an extension - but didn't rule it out Wednesday.
However, a fraught weekend in Brussels culminating in UK Brexit Secretary Dominic Raab walking away from the negotiating table means a deal won't be signed off until November - if there is a deal at all.
British Prime Minister Theresa May said Wednesday that "now is the time" to make a Brexit deal happen, but officials said she failed to offer new proposals to break the impasse at a crucial Brussels summit.
"There are issues remaining around the backstop", May told reporters on Thursday, referring to the debate over how to form a customs border between Ireland - which will remain in the European Union - and the U.K.'s Northern Ireland, without establishing a hard border between the two.
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.
Lithuanian President Dalia Grybauskaite said that 2 ½ years after Britain's Brexit referendum, the country had still not explained clearly how it wants to leave the EU.
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Her difficulties were laid bare by the fury sparked back home at her suggestion that she could extend a post-Brexit transition period to address the fraught issue of the Irish border.
The mooted extension to the transition period is a new idea being put forward by the European Union to help Theresa May square the circle created by the written agreement last December and the draft withdrawal agreement in March.
The US administration has notified Congress that it will seek trade pacts with the EU, Japan and Britain.
However, with her party split, and some Tory MPs openly calling for her to go, Mrs May has little room to manoeuvre if she is to secure a deal which stands any chance of getting through Parliament.
"She's between a rock and a hard place", Finland's former prime minister Alexander Stubb said of May, in an interview with NPR's Morning Edition.
"Now all of them are trying to distance themselves from the time bomb they created a year ago", he said.
But this issue is causing a major stumbling block in finalising any Brexit deal.
Juri Ratas, the Estonian Prime Minister, struck a more sympathetic tone.
"Mrs. May recalled the importance of a UK-wide customs territory". The boundary has been largely invisible since the 1998 Good Friday Agreement, which ended decades of sectarian violence known as the Troubles, and both sides have said they want to avoid any return to a hard border. May spoke of "working intensively over the next days and weeks" to achieve agreement that avoids a no-deal departure from the bloc for Britain on March 29 that could create chaos at the borders and in the economy.