MANCHESTER, England — Prime Minister Boris Johnson of Britain presented to the European Union on Wednesday what his aides billed as a final offer on Brexit, but the swift, negative response of Irish officials to the plan suggested it would not draw the two sides any closer to an amicable divorce.
Speaking at the Conservative Party conference in Manchester, Mr. Johnson insisted that Britain had compromised in its offer, the details of which were transmitted to Brussels on Wednesday afternoon. He asked the European Union to compromise, too, he said, insisting that an orderly British exit could be the beginning of a new relationship with Europe.
“It cannot be stressed too much that this is not an anti-European party and it is not an anti-European country,” Mr. Johnson said. “We love Europe. We are European.” When the audience failed to clap, the prime minister added somewhat awkwardly, “At least, I love Europe.”
In a freewheeling address on the final day of the conference, Mr. Johnson vowed again to lead Britain out of the European Union by Oct. 31, with or without a deal. He cast the departure as a litmus test for British democracy, warning that any further delay would flout the will of the public.
“People are beginning to feel that they are being taken for fools,” Mr. Johnson said. “They are beginning to suspect that there are forces in this country that simply don’t want Brexit delivered at all. And if they turn out to be right in that suspicion, then I believe there will be grave consequences for trust in democracy.”
Mr. Johnson’s gleefully combative tone seemed calculated less to break a deadlock with the European Union than to mobilize the party’s rank-and-file for a coming election that he hopes will give him a popular mandate to negotiate with Brussels from a position of greater strength.
The prime minister framed his struggle in populist terms: the people vs. Parliament. He heaped ridicule on lawmakers for thwarting his efforts to push for a “no deal” Brexit and to call an election. If Parliament were a reality television show, he said, “the whole lot of us would have been voted out of the jungle by now.”
The prime minister was scheduled to speak later on Wednesday with the president of the European Commission, Jean-Claude Juncker, about the details of Britain’s latest offer. The plan, dubbed “two borders for four years,” would pull Northern Ireland out of the European customs union along with Britain but leave much of the territory’s economy aligned with European Union regulations for a period.
Irish officials rejected the proposal, which would still require checkpoints to monitor trade in goods between Northern Ireland and the south, and said it raised questions about whether Mr. Johnson was negotiating in good faith. Ireland’s acquiescence is viewed as necessary to winning the approval of the European Union.
Mr. Johnson also outlined his likely pitch to voters for when the election everyone expects finally arrives. After leaving the European Union, he said, his government would focus on domestic priorities including education, tackling crime, creating more housing, building infrastructure and investing in health policy.
“It is time for us to say loud and clear: We are the party of the N.H.S.,” Mr. Johnson said, referring to the National Health Service, which offers mainly free health care and was created after World War II by the opposition Labour Party, which voters trust more to protect it.
The prime minister’s claim was a direct challenge to the opposition, led by the left-wing leader Jeremy Corbyn, whom Mr. Johnson attacked in a passage that offered a preview of the Tories’ election strategy.
“If Jeremy Corbyn were allowed into Downing Street, he would whack up your taxes, he would foul up the economy, he would rip up the alliance between Britain and the U.S.A., and he would break up the United Kingdom,” Mr. Johnson said.
By turns irreverent and impassioned, Mr. Johnson drew laughter and applause from his audience. He cheerfully mumbled his way through discussions of scientific investments and likened Mr. Corbyn to Konstantin Chernenko, the aging, infirm Soviet leader who stumbled into office in the 1980s.
“Look it up,” he told the mystified crowd.
It was a far smoother performance than that by his predecessor, Theresa May, whose trouble-prone appearance two years ago — when she was interrupted by a prankster and seized by a coughing spasm, and parts of the stage set collapsed behind her — became a metaphor for the party’s broader disarray.
But Mr. Johnson’s rallying cry for Brexit offered no road map to a compromise with Brussels. If anything, it could merely serve to set the stage for a round of recrimination if the negotiations fail to produce a deal in time.
The plan, analysts said, will never pass muster in Ireland. The country’s prime minister, Leo Varadkar, would find it impossible to accept the construction of customs checks on the island of Ireland even if they were tucked well away from the border, they said, because of fears that such facilities would become a target for terrorists.
“British Conservatives need to think more about Irish politics,” said Charles Grant, the director of the Center for European Reform, a research group. For now at least, he said, Germany and France would not force Ireland into a deal it does not want.
Mr. Johnson has always been a darling of the Tory conference. Yet, while activists have united behind his promise to “get Brexit done” by the October deadline and are confident that they have the populist messages to win a general election, the mood at the conference was at times uncomfortable.
Some Conservatives view Mr. Johnson as an effective communicator and someone who has at last given them a strategy that could work with voters after the disarray of Mrs. May’s premiership.
But they know that their path out of the bloc under Mr. Johnson’s leadership could be a roller-coaster ride. There is also unease about his inability to keep stories about his relationships with women off the front pages of the tabloid newspapers.
“There are two vibes here,” said Sophia Gaston, the managing director of the British Foreign Policy Group, a research institute, “a triumphant sense of energy and momentum putting the party on course to win a majority in a general election, and a sense of profound precariousness and that things could fall apart.”