Citing May's reported preference for an extension of the Withdrawal Agreement transition period, Tajani told reporters, "Reference has been made to three, not two, years and we are in favour of this".
Former Northern Ireland secretary Owen Paterson, former Conservative leader Iain Duncan Smith and former first minister of Northern Ireland Lord Trimble will be joined by Hans Maessen, former president of the Dutch customs association, and Shanker Singham, from the Institute of Economic Affairs. "Now that is not an acceptable way for a leader of a government to behave".
What is the transition period and what's being suggested?
With little progress in negotiations and worst-case scenarios seeming more likely, NPR's Soraya Sarhaddi Nelson reports, "European leaders say they are working on contingency plans for a United Kingdom departure from the bloc without a deal on how to manage critical issues like borders, customs and air traffic control".
But Mrs May did not come forward with the new "concrete proposals" on the border issue which European Council president Donald Tusk said were needed to break the deadlock.
"I think we are both of the understanding that [the backstop] is an insurance policy and obviously we want to address all of these issues in a future relationship", Helen McEntee, Irish Taoiseach (prime minister) Leo Varadkar's Europe minister, told BBC Radio Ulster's Good Morning Ulster programme, following intra-EU discussions.
He acknowledged that "it may be a more emotional impression than a rational one. As you know emotions matter in politics", said Tusk.
"I am open to the idea of an extension or a longer transition period, but that's not an alternative to a legally binding Irish backstop, so it's certainly not an alternative; it's something that might be part of the mix", he said.
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"We are working to ensure that we have that future relationship in place by the end of December 2020", May said as she arrived Thursday at European Union headquarters in Brussels for meetings on migration, security, and other issues.
Britain's Brexit minister, Dominic Raab, said just a week ago that the so-called backstop created to prevent a hard border between the British province of Northern Ireland and the Republic of Ireland, must be finite, short and time-limited.
The Irish and the European Union will also still need the backstop in the withdrawal agreement, which must be signed before the business of the trade deal can get under way.
With the deadlock, this week's summit, which had been billed as a make-or-break moment, turned simply into a chance for Britain and the European Union to give themselves more time _ perhaps until the end of the year _ to break the logjam.
At least 30,000 people cross the border every day for work, with many residents of border regions living on one side and working on the other. They have spent far more time arguing with themselves than negotiating with the EU.
In a speech to the German parliament before travelling to Brussels, Chancellor Angela Merkel said that the possibility of a Brexit deal was "still there", but added that Berlin was making plans for a no-deal withdrawal.
But, she added; "Where there's a will, there should be a way, and normally there is a way".
The senior source said the leaders agreed talks should continue but, for now, they are "not planning to organise an extraordinary summit on Brexit in November".