BRUSSELS (AP) — British Prime Minister Theresa May opened a Brexit summit Wednesday seeking to convince fellow European Union leaders her plans for a friendly divorce were not dead and that a deal can be achieved in weeks, despite the bloc's calls for her to come up with a new approach.

The prime minister's high-stakes diplomatic mission started with a handshake and a kiss on the cheek from the president of the EU's executive branch, Jean-Claude Juncker. Meeting with Juncker was the first of several one-on-one meetings on May's schedule before she addresses her 27 EU counterparts on bringing the negotiations over Britain's departure to completion.

Ahead of the pre-dinner speech, May said "everybody around the table" wanted an agreement for an orderly U.K. withdrawal, and "by working intensively over the next days and weeks I believe we can achieve a deal."

May was also meeting European Council President Donald Tusk, who a day earlier implored May to present new ideas at the summit for resolving the sticky problem of how to keep the border between the Republic of Ireland and the U.K.'s Northern Ireland friction-free once Britain no longer is an EU member.

Tusk advised May that "creative" thinking from Britain was required to avoid a hard border on the island of Ireland, the issue that has brought divorce negotiations to a standstill. EU leaders dismissed May's most recent proposal as unworkable.

But when the prime minister was asked in the House of Commons earlier Wednesday whether her government's blueprint for an amicable exit was dead, May replied: "The answer is no."

Because of its timing, the summit in Brussels was billed long in advance as the "moment of truth" in the two-year Brexit process. But after urgent talks on the Irish border Sunday ended without producing the hoped-for breakthrough, the gathering looked more like a therapeutic bonding session than an occasion to celebrate.

The timeline for a deal has slipped into November, or even December, when another EU summit is scheduled.

"Today there will be no breakthrough," said Lithuanian President Dalia Grybauskaite. She said that two-and-a-half years after Britain's referendum the country had still not explained clearly how it wants to leave the European Union.

"Today we do not know what they want," she said. "They do not know themselves what they really want. That is the problem."

Britain leaves the EU on March 29, but a deal must be sealed soon so parliaments have time to give their verdict. Failure could see the U.K. crash out without agreement, with huge disruption to trade, travel and daily life.

May planned to accentuate the positive when she addresses fellow EU leaders — before they have dinner without her — by stressing how much progress has been made in many areas. She told reporters that "most of the issues" in the withdrawal agreement have been resolved — apart from the Irish border.

At present the two sides are proposing that Britain remain inside the EU single market and bound by its rules from the time it leaves the bloc in March until December 2020, to give time for new trade relations to be set up.

Many suspect that will not be enough time, which has led the EU to demand a "backstop" to ensure there are no customs posts or other controls along the currently invisible border between the U.K.'s Northern Ireland and EU member Ireland. Disagreement over the backstop has brought divorce negotiations to a standstill.

Irish Foreign Minister Simon Coveney said EU chief negotiator Michel Barnier had suggested "more time in the transition period to agree an alternative solution to a backstop."

The idea is to give the U.K. enough time to negotiation new customs arrangements so that the backstop is never likely to be used, he told the BBC.

Britain says it has not asked for an extension, but May has not yet come up with proposals for unblocking the border logjam. She is hemmed in by pro-Brexit members of her Conservative Party, who oppose any more compromises with the bloc, and by her parliamentary allies in Northern Ireland's Democratic Unionist Party, who insist a solution to the border issue can't include customs checks between Northern Ireland and the rest of the U.K.

German Chancellor Angela Merkel said Wednesday that she still believes it's possible to conclude a "good and sustainable" agreement with Britain before its departure — but stressed Germany also is preparing for the risk of a no-deal departure.

Meanwhile, the top EU trade official played down the importance of a U.S. announcement that it will pursue a trade deal with Britain, noting London cannot negotiate such pacts until it leaves the bloc.

The U.S. administration has notified Congress that it will seek trade pacts with the EU, Japan and Britain. President Donald Trump has long said he wants a deal with Britain, even as it negotiates a messy EU exit.

EU Trade Commissioner Cecilia Malmstrom noted Wednesday that "the U.K. cannot negotiate any trade agreement as long as they are a member of the European Union."

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Geir Moulson in Berlin contributed to this story.