"I look forward to intensifying, heating up the negotiations and making sure we re in the best position to get the best deal", Raab told reporters, standing next to Barnier.
The comments come after Mrs May survived a series of knife-edge Commons votes which had the potential to sink her fragile premiership.
That is the deadline when a transition period is due to end after Britain and the European Union agreed to continue working together after Britain formerly leaves next March.
Former Foreign Secretary Boris Johnson read out a personal statement in Commons earlier in which he took a veiled swipe at Russian Federation, outlined his opposition to Theresa May's Brexit plan, and said "it's not too late to save Brexit".
British voters in a June 2016 referendum chose to leave the European Union, and on Tuesday Britain's official Brexit campaign, Vote Leave, was fined and reported to the police for breaking spending rules - another issue boosting calls for a second vote.
"And if we can't find a solution, I don't know how to bring Brexit to the goal", Asselborn said.
With Brexit negotiations at an impasse largely because the British government is struggling to command a majority in parliament, there is growing concern that the country could end up crashing out of the European Union without a deal.
Johnson, the former mayor of London seen to have ambitions to be prime minister, is not alone in calling for May to ditch the Chequers plan.
Shouts rang out across the Commons.
Even Davis jumped into the bad-tempered exchanges, asking May to publish the legal draft of a free trade treaty.
Mr. Davis' former deputy, Steve Baker, asked about contingency plans for a no-deal departure.
The session offered a mirror on a party deeply split and a government just scraping by to stay in power. We want to have an ambitious partnership with Britain, we want to work with Britain on a trade agreement and on internal and external security because it is a very important partner for us. It was not the plan agreed by the government earlier this month at May's country retreat at Chequers, he said.
Boris Johnson put the Prime Minister on notice to scrap a Brexit strategy he claimed would leave the United Kingdom in a "miserable permanent limbo", or face being ousted from Downing Street.
"It is not too late to save Brexit", Mr Johnson added.
May will be back in the firing line on Wednesday when she takes questions from lawmakers in parliament before appearing in front of a parliamentary committee, and then leading a Conservative Party meeting.
Theresa May faces further threats to her government's Brexit strategy and could have to stave of the prospect of a "no confidence" challenge to her leadership this week, after revealing that Donald Trump's had advised her to "sue" the EU. "We need an all-weather insurance policy".
Davies has submitted a letter of no confidence in the PM to the chair of the backbench 1922 Committee over her "unacceptable" post-Brexit trade deal, according to the Yorkshire Post.
The government has tabled a motion suggesting that parliament's summer recess should begin on Thursday, five days earlier than originally planned.