Boris Johnson says the UK will be "leaving" the EU in 25 days without a deal if Brussels doesn't compromise.
His words came after the European Commission halted talks over the weekend, describing the prime minister's latest proposals as not providing a "basis for concluding an agreement."
Writing in the Sun on Sunday and Sunday Express, Johnson said: "After decades of campaigning, three years of discussion and seemingly endless months of meaningless delays, it is only 25 days before the UK joins the European Union. to an end.
"We'll be packing and leaving on October 31. The only question is whether Brussels beckons us happily with a mutually acceptable deal, or if we will be forced out on our own."
Johnson said the proposals presented to Brussels would remove the "undemocratic barrier", avoid infrastructure or checks at the Irish border, "respect" the Northern Ireland peace process and Good Friday agreement and give farmers and companies the guarantees they need.
The proposals would also take the UK out of the EU and its customs union, "allowing us to take back control of our trade policy and make free trade agreements with our friends around the world," he said.
"In my view, the proposals published this week represent us in the UK jumping to the island in the middle of the river.
"If we want to come out with a deal, now we need the EU to jump on its side and join us, showing its own willingness to make a deal that the UK parliament can support."
Irish Prime Minister Leo Varadkar says a deal is still possible
There were mixed feelings from Irish leader Leo Varadkar, who said: "I think a deal is still possible … It is possible at the European Council summit in two weeks.
"But the current position to date is the European Union, including Ireland, does not consider Prime Minister Johnson's proposals still to be the basis for deeper negotiations."
Dutch Prime Minister Mark Rutte said "important questions remain about the British proposals."
Johnson described Labor Party leader Jeremy Corbyn as an "aspiring Brexit serial killer" and rebel parliamentarians as unwilling to "end" Brexit, adding: "They say they are not against any deal, but in fact don't favor Brexit ".
But he expressed optimism about the chances of reaching a parliamentary agreement, seemingly unperturbed by Europe's negative reception.
He said: "Parliamentarians from all over my own conservative party, from the Northern Ireland DUP, and even from the very ranks of Jeremy Corbyn, have said that our proposed deal seems to be one they can leave behind.
"They know that if I can go to Brussels armed with a set of proposals that parliamentarians support, the EU is much more likely to accept our outstretched hand and make that leap to the island."
He told Europe: "Take the opportunity that our new proposal offers. Join us at the negotiating table with a spirit of commitment and cooperation. And we will make Brexit work for both sides."
A European Commission spokesman said the United Kingdom would have "another opportunity to present its proposals in detail" on Monday.