Tajani said he raised with May the possibility that the post-Brexit transition period, during which Britain would retain European Union rules and avoid border problems with Ireland, could be extended by a year to 2021 - something European Union negotiators proposed to soften a demand for special rules for Northern Ireland.
His comments come days after reports that Brexit talks have run into a "significant problem" over the issue of the Northern Ireland border.
The Democratic Unionist Party, which is propping up Mrs May's government in Westminster, said the EU's backstop suggestion whereby Northern Ireland would continue to follow the bloc's rules if no trade deal is struck would create barriers with Great Britain.
Instead, the matter could either be pushed back to December or - more dramatically - the European Union could use the November weekend to meet on preparations for a "no-deal" Brexit.
The meeting in Brussels was supposed to be the occasion when the leaders of the European Union 27 member states gave the green light for a special summit in November to finalise the terms of Britain's withdrawal.
Her official spokesman later told reporters: "The Cabinet strongly supported her on the importance of maintaining the integrity of the Union and agreed that we must ensure we can not be kept in a backstop arrangement indefinitely".
"Later at 27, we will decide on how to take the negotiations forward, on the basis of a recommendation by our chief negotiator, Michel Barnier".
May was preparing to address other EU leaders one day after European Council President Donald Tusk implored her to present new ideas for resolving the tricky problem of how to keep the land border between the Republic of Ireland and the U.K.'s Northern Ireland friction-free once Britain no longer is an EU member.
BBC political correspondent Nick Eardley, in Brussels, said European Union sources suggested the PM had given a "relatively positive assessment" and while there was goodwill on both sides "we are not where we would have liked to be".
The return to a hard border in Northern Ireland would be a "political failure" by both the British government and the European Union, a former head of the Army has said. Brexit must be orderly for everyone and for all the issues including the island of Ireland.
The cabinet meeting yesterday did not consider a specific wording on any deal, nor make any decisions, but was a discussion about the negotiations and unity.
"I don't think it will happen, I don't want it to happen, it would be a disaster if it did happen, it must not happen".
"Any informed person knows that the Northern Ireland Office has just completed an extensive consultation on the legacy of the past, which is something that we are still finding very challenging 20 years on from the Good Friday Agreement", she continued. She said: "We realise that the technical agreement of last week was not accepted in London".
Michael Gove admitted today the Brexit deal might not be done until December.
"We want to secure a deal as quickly as possible".
However, a senior United Kingdom official insisted: "the prime minister has a clear mandate to negotiate and there is a clear position which has been set out, which the cabinet is firmly backing".
Tusk has made it clear that if May and Barnier do not offer signs of concrete progress towards a draft deal he will not call a November summit to sign it. Emmanuel Macron, the French president, said the need for progress was "urgent".
At a three-hour cabinet meeting on Tuesday morning, which included ministers with reservations about her strategy, May said a deal was possible if they all stood together.
He had apparently drawn the wrath of the Saudi government, which has become an ever-closer US ally under President Donald Trump . To reporters, to anybody. "We can not let this happen, to reporters, to anybody", Trump said.
In addition, I have directed our Public Safety & Homeland Security Bureau to promptly initiate an investigation into this matter. At least 27 deaths have been blamed on the hurricane across four USA states - a number expected to increase further.
Local media reported shots being fired inside the station, something which a police spokesperson later denied. She said: "We assume that a hostage has been taken, either at McDonald's or at a nearby pharmacy".
Warren for years has been accused of exaggerating her Native American heritage to help get a job as a Harvard law professor. This is in part because Native American leaders have asked tribal members not to participate in genetic databases.
The CDC received information on 33 confirmed cases of AFM across 16 states in 2017, 149 cases in 39 states. In most cases, the patient's arms or legs become weak, similar to the results of infection with polio .
Khashoggi , an outspoken critic of the regime, hasn't been seen since entering a Saudi consulate in Islamabad on October 2. BBC News report that a Turkish security source has video and audio proving Khashoggi was killed inside the consulate.
Sony is yet to respond to the reports, but follow the above and you should be safe until a likely security patch is released. I hope anyone that's affected by this can easily reset their factory settings and get back up and running smoothly.
Trump tells AP he won't accept blame if GOP loses House
Hear what President Trump has to say about some of the issues that will likely be motivating voters at the ballot. But I definitely want to do new photography, and I want to move away from at least USA politics for sure.
Portugal issues red alert for rare Atlantic hurricane
The storm could produce flash flooding in portions of Portugal and Spain and life-threatening surf and rip current conditions. In October 2017, strong winds from passing Hurricane Ophelia fed forest fires that killed around 40 people during a heatwave.
10 kids diagnosed with rare polio-like illness in Illinois
EV-D68 infection most commonly results in mild symptoms such as runny nose, sneezing, cough, body aches and muscle aches. Preventing AFM can start by protecting yourself and children from poliovirus by getting vaccinated, according to the CDC.
Bearish Sentiment Returns To Oil Markets
Michael crashed ashore Florida on Wednesday as the third most powerful hurricane to strike the United States mainland. The Organization of the Petroleum Exporting Countries ( OPEC ) made a similar move on Thursday.
Sears craters after filing for bankruptcy (SHLD)
Three companies that sell items at Sears told Reuters this week that Sears had missed payments to them over the past few weeks. With Sears heading toward bankruptcy, any potential for liquidation could mean an end to the lease agreements with Seritage.
James Murdoch could take chairman role at Tesla
However, Gracias may not be sufficiently independent as he is invested in other companies linked with Musk, including SpaceX . Tesla's board has become a source of contention with the SEC and investors, with some viewing it as too close to Mr Musk.
India elected to UN human rights body
India received 188 votes, the highest polled by any of the 18 countries elected from the 193-member General Assembly . Among the other candidates, Eritrea has obtained 160 votes, Somalia 170 votes and the Bangladesh 178 votes.
Himalayan storm: Climbers' bodies removed from Nepal mountain
A helicopter was sent to investigate and spotted the bodies, but strong winds prevented the rescue team from retrieving the dead. A group of South Korean climbers and their guides have died on Nepal's Mount Gurja after a violent snowstorm hit their camp.
Manchester United plot third move to sign Aaron Ramsey
Asked if he would give Ramsey a new deal in the circumstances, Wenger replied: 'We tried that before and it still can happen'. The Gunners will take on Leicester City in their next top flight fixture at the Emirates Stadium after the worldwide break.
Umpire Angel Hernandez goes 1-for-4 on replay reviews
New York's bullpen has allowed one run in 10 innings, led by Dellin Betances , Zach Britton and Aroldis Chapman . Jonathan Holder allowed one run in two innings, making him New York's most effective pitcher in the game.