Boris Johnson has said he “won’t be deterred by anybody” from leaving the EU on 31 October.
The prime minister said he was “cautiously optimistic” of getting a Brexit deal, but the UK would leave by the deadline “whatever happens”.
EU chief Brexit negotiator Michel Barnier said he did not have “reasons to be optimistic” over getting a deal.
Mr Johnson will meet him and European Commission President Jean-Claude Juncker on Monday for talks.
The PM’s comments come after Parliament passed a law forcing him to ask for an extension to Brexit.
Mr Johnson will have to write to the EU on 19 October to ask for an extra three months, unless he returns with a deal – then approved by MPs – or gets the Commons to back a no-deal Brexit.
But despite the new law, Mr Johnson said he would rather be “dead in a ditch” than ask for an extension.
MPs managed to pass the law before Parliament was suspended – or prorogued – in the early hours of Tuesday morning until 14 October.
Mr Johnson said the government had made the move so it could hold a Queen’s Speech and put forward its new domestic policy agenda.
But opposition MPs claim it was to stop scrutiny in Parliament of his Brexit plans.
Earlier this week, a Scottish court ruled the prorogation was unlawful as it was motivated by an “improper purpose of stymieing Parliament”.
The government is appealing against the decision and a ruling will be made by the Supreme Court in London on Tuesday.
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