"I think it's absolutely vital that we focus on getting the right deal in the future and making sure in the areas that matter so much to the British people we can get a good outcome".
Barnier stressed it was Prime Minister Theresa May's British government that requested the extension option and warned: "It can't be indefinite".
He told Sky News Sunday that his party will vote against the deal and demanded that May return to Brussels and renegotiate the divorce agreement.
She said the Environment Secretary had been doing "a great job", adding: "I haven't appointed a new Brexit Secretary yet, but obviously I will be doing that over the course of the next day or so".
Following the 2017 election, the United Kingdom's Conservative government is a minority administration which is kept in power through a "supply and confidence" agreement with the Northern Irish regional group the DUP.
TRT World's Simon McGregor-Wood has more. "She could be leading them to a very bad place".
"And let no one be in any doubt - I am determined to deliver it", she said.
That steadfast message resonated with delegates, triggering extended applause.
When struck, the deal meant the smaller party would support the government on key votes including the Queen's Speech, the budget, and finance bills, allowing the administration to survive without enough of their own parliamentarians to otherwise run a stable government.More news: YouTube quietly adds 100 movies for free viewing
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British media are reporting that 42 lawmakers in May's Conservative Party had given firm assurances that they had submitted no-confidence letters, short of the 48 needed.
He said: "We now need to keep up the momentum to finalise the withdrawal agreement and outline political declaration and deliver a Brexit that works for the whole United Kingdom".
May added that the next seven days "are going to be critical" for successful Brexit talks, and that she will be traveling to Brussels to meet with EU leaders before an emergency European Council summit on November 25.
European ministers signed off on Britain's draft divorce deal on Monday as they launched a "painful" final week of negotiations on future cross-Channel ties.
Several ministers, including her Brexit minister, have resigned and many of her lawmakers seeking to oust her.
May's government relies for survival on the votes of Northern Ireland's Democratic Unionist Party, which struck a deal past year to back the Conservatives on major legislation, including finance bills.
May has vowed to fight on, but with both pro-EU and pro-Brexit lawmakers unhappy with the draft agreement, it is not clear if she will be able to win the backing of parliament for it, raising the risk of Britain leaving the European Union without a deal.
"These negotiations have been tough right from the start, but they were always going to get more hard towards the end", May told Sky News on Sunday.
One caller to the half-hour grilling on LBC told the PM that Jacob Rees-Mogg would make a better leader, while another said she had "appeased" the European Union like Neville Chamberlain in his negotiations with Hitler.