Senior British government minister Michael Gove has insisted the UK will leave the EU by 31 October, despite the government asking the EU for a delay.
Asked if he could guarantee that the UK would leave the EU by Halloween, Mr Gove, who is in charge of no-deal preparations, said: "Yes, that's our determined policy. We know that the EU want us to leave, we know that we have a deal that allows us to leave."
Mr Gove told Sky News: "We are going to leave by October 31st. We have the means and the ability to do so and people who - yesterday we had some people who voted for delay, voted explicitly to try to frustrate this process and to drag it out.
"I think actually the mood in the country is clear and the prime minister's determination is absolute and I am with him in this, we must leave by October 31st."
Meanwhile, EU leaders are considering a request by Mr Johnson to delay Britain's departure from the bloc, which he was forced to make after MPs refused to back his Brexit deal.
Mr Johnson has pinned his premiership on getting Britain out of the EU on 31 October, more than three years after the 2016 referendum vote for Brexit.
But the House of Commons yesterday refused to support a divorce deal he struck with Brussels last week, triggering a law demanding he ask to delay Brexit to avoid the risk of a damaging "no deal" exit.
He sent a second letter - signed - warning that "a further extension would damage the interests of the UK and our EU partners".
A defiant Mr Johnson had earlier told MPs: "I will not negotiate a delay with the EU."
Mr Tusk said he would begin consulting EU leaders "on how to react" - a process one diplomat said could take a few days.
Mr Johnson has already spoken to the leaders of France, Germany and the Netherlands to press his case - and Paris warned yesterday that a Brexit delay was "in nobody's interest".
In the meantime, Mr Johnson will bring forward legislation that he hopes would nevertheless allow Brexit on 31 October.
MPs voted to withhold approval for his divorce deal unless and until the legislation required to ratify the treaty is passed through parliament.
The government is seeking a new vote on its deal tomorrow, although this may fall foul of parliamentary procedure.
If it introduces the treaty implementation bill tomorrow, however, MPs could be called to vote as early as Tuesday.
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Mr Johnson wrote to Mr Tusk that he was "confident" he could get it through before the end of the month.
However, the main opposition Labour Party has condemned the deal as a "sell-out", while the DUP is opposed to its arrangements for Northern Ireland.
Mr Johnson sent the letter to Brussels after a day of high drama in the Commons, which staged its first Saturday sitting in 37 years to debate his Brexit deal.
He urged MPs to end years of uncertainty that has weighed on the economy and divided the nation - but they refused, warning his deal would leave Britain worse off.
"Why won't they let us leave?" lamented the Brexit-backing Sunday Express newspaper.
The Mail on Sunday led with the headline 'The House of Fools', warning MPs had "subjected us to yet more agonising delay".
The Brexit date has already been pushed back twice, to the fury of those who wanted to chart their own course and abandon the European project after nearly 50 years.
But there was also jubilation at the vote among tens of thousands of protesters who gathered outside parliament yesterday to demand a new referendum to reverse Brexit.
"That's really good, that's one step away from Brexit," demonstrator Philip Dobson told AFP.
"Reject Brexit", "Put It To The People" and "Stop This Madness" read some of the placards at the mass march, where many protesters also waved EU flags.
Mr Johnson took office in July vowing to leave the EU on 31 October come what may.
But MPs fearful of the risks of a "no deal" departure sought to bind his hands, with a law demanding he delay Brexit if he failed to get an agreement approved by 19 October.
The amendment passed yesterday is designed specifically to avoid this scenario.
MPs had feared they might pass the Brexit deal but then get bogged down with the laws needed to implement it, risking Britain accidentally crashing out of the EU at the end of the month.
Additional reporting PA