The Irish border is the major sticking point blocking a deal.
"I'm clear that it is possible to do that and that is what we are working for".
A spokesperson for the Alliance Party said: "We are disappointed by the prime minister's refusal to engage with the remain parties collectively".
Tajani said the European Parliament, which must endorse any Brexit deal sealed between London and the EU for it to take effect, was in favour of extending the post-Brexit transition period to three years from 21 months.
Tusk also said the leaders expressed their resolve to stop the flow of illegal migration.
The Foreign Secretary also called on his party to unite behind the Prime Minister as the negotiations enter the final phase. "Such a regime should help to protect our citizens, companies and institutions from all kinds of cyber security threats", he said.
Tom Newton Dunn, political editor of the Sun newspaper, commented that May saying a transition extension would only be for a few months feels like the "I'm only half pregnant" defense.
He also said there would be "huge difficulties" within the European Union 27 member states to consider making the backstop UK-wide, adding that the European Union is willing to make exceptions to treat Northern Ireland as a special case because of its hard history and unique geography.
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But he said she was "not against" the idea of extending the transition, a position confirmed by the European Union official.
Britain's foreign minister Jeremy Hunt said on Friday it would be hard to resolve the issue of a backstop to the Irish border problem in Brexit talks with the European Union without more detail on their future relationship.More news: Liverpool's Sadio Mane undergoes surgery on broken left thumb
"What we are doing is working to ensure we have a solution to the backstop issue in Northern Ireland, which is now a blockage to completing the deal".
The EU's guidelines on negotiations for Britain's future relationship with the bloc had granted Spain veto rights over the issue of Gibraltar, making it a potential difficulty.
Its co-chair Richard Tice said: "The original transition was an unnecessary trap created by our weak civil servants who can not be trusted as they don't want us to leave.
She accepted the dictates as to how the negotiations would take place and the sequencing of them by the European Union".
And negotiating some kind of alternative arrangement with Northern Ireland could cause cracks to form in the U.K.'s constitutional unity with Scotland, writes the Financial Times.
British opponents of Brexit say the United Kingdom won't be able to strike a trade deal with the USA unless it weakens its current EU-level protections on workers rights, animal welfare and environmental protection.
Irish premier Leo Varadkar has warned that businesses in the United Kingdom will soon make decisions that "bite" after admitting that reaching a Brexit deal could roll into the new year.
Britain leaves the European Union on March 29, but a deal must be sealed soon so parliaments have time to give their verdict.
At the meeting in Brussels, EU leaders decided that not enough progress has been made in negotiations to warrant calling a one-off summit in November for a divorce deal to be signed.
Syed Kamall, the leader of the Conservative's group, is "quite confident that there will be a deal by the end of the year", a spokesperson said on Friday. "They do not know themselves what they really want".
Simon Collins, the Executive Officer of the Shetland Fishermen's Association, warned the Government it should not let fishermen down again - insisting the key issue between the fishing industry and the UK Government remains to be "trust" in Brexit talks.
Both sides think an extension would allow for more time to find a solution to the Irish border.