The Prime Minister said he believes “passionately” that a new Brexit deal can be struck with Brussels ahead of his meeting with the European Commission president.
Mr Johnson will use the meeting in Luxembourg to underline his opposition to delay to Britain’s departure - despite the legislation passed by Parliament requiring him to seek an extension in order to avoid crashing out without a deal on Halloween.
He said: “If we can make enough progress in the next few days, I intend to go to that crucial summit on October 17 and finalise an agreement that will protect the interests of business and citizens on both sides of the Channel, and on both sides of the border in Ireland.
“I believe passionately that we can do it, and I believe that such an agreement is in the interests not just of the UK but also of our European friends.
“We have all spent too long on this question. And if we can get that deal, then of course there will be time for Parliament to scrutinise and approve it before the end of October.
“But be in no doubt that if we cannot get a deal - the right deal for both sides - then the UK will come out anyway.”
The PM will also hold talks with Luxembourg’s prime minister Xavier Bettel and the EU’s chief negotiator Michel Barnier on Monday.
A Number 10 source said: “The Prime Minister could not be clearer that he will not countenance any more delays. We will be leaving on October 31 - no ifs, no buts.”
The law passed by Parliament after MPs seized control of Commons business requires the Prime Minister to seek an extension to the Brexit process if a deal has not been reached by October 19.
“The UK Government is always going to behave lawfully,” he told BBC Radio 4’s Today.
“I think the suggestion otherwise is nonsense.
“We, of course, take these considerations very seriously.
“At the same time, the legislation that was required, the surrender bill, is deeply, deeply flawed.”
Downing Street has sought to downplay speculation that Monday’s meeting could be a breakthrough moment, and Brexit Secretary Steve Barclay said on Sunday that while there was still “significant work” to do to reach an agreement, a “landing zone” for a deal was in sight.
Finland’s European affairs minister Tytti Tuppurainen said the UK still had not put forward any proposals that could “compensate” for the removal of the Irish backstop.
“Of course the European Union is always ready to negotiate when a proper proposal from the United Kingdom side is presented,” she said.
Over the weekend, Mr Johnson likened Britain leaving the EU to the Incredible Hulk, telling the Mail On Sunday: “Hulk always escaped, no matter how tightly bound in he seemed to be - and that is the case for this country.”
But his comparison was described as “infantile” by the European Parliament’s Brexit co-ordinator Guy Verhofstadt, who questioned: “Is the EU supposed to be scared by this?”
And former justice secretary David Gauke told Today: “Maybe the Incredible Hulk doesn’t have to comply with the law, but the British Government does.
“And if Parliament has neither supported a deal, nor supported a no-deal departure, then the law is clear that he has to seek an extension, the Prime Minister has to seek an extension, and that is what he will have to do.”