BRUSSELS (Reuters) - British Prime Minister Theresa May made clear her desire on Thursday to move Brexit talks forward to a discussion of a future trade relationship at a dinner with EU leaders who applauded her for progress made so far.

A day after she suffered a defeat in parliament over her blueprint for quitting the EU, May told her peers at a summit in Brussels that she was on course to deliver Brexit and urged them to speed up the talks to unravel more than 40 years of union.

Offering her reassurance that they will endorse on Friday the launch of a second phase of negotiations on a free trade pact and an initial transition period, leaders responded to May’s remarks by a brief round of applause before she was to leave the summit to allow them to discuss Brexit without her.

A British government official said the prime minister made “no secret of wanting to move on to the next phase and to approaching it with ambition and creativity”.

“I believe this is in the best interests of the UK and the European Union,” she told the leaders over a dinner of roasted langoustine and capon chicken. “A particular priority should be agreement on the implementation period so we can bring greater certainty to businesses in the UK and across the 27,” she added.

Officials said German Chancellor Angela Merkel congratulated May on bringing the negotiations last week to the stage of “sufficient progress” that will enable leaders to accept opening the next phase of talks.

Summit chair Donald Tusk will call May on Friday to update her after leaders have discussed their next moves on Brexit.

May, weakened after losing her Conservative Party’s majority in a June election, has so far carried her divided government and party with her as she negotiated the first phase of talks on how much Britain should pay to leave the EU, the border with Ireland and the status of EU citizens in Britain.

But the second, more decisive phase, of the negotiations will further test her authority by exposing the deep rifts among her top team of ministers, or cabinet, over what Britain should become after Brexit.

Acknowledging tough talks ahead, Tusk warned them that only the unity they had displayed so far would deliver a good deal on trade -- an issue on which the member states have different interests: “I have no doubt that the real test of our unity will be the second phase of Brexit talks,” he told reporters.

May’s team was upbeat.

“Look at what’s been achieved so far. The deal on phase one which many commentators said couldn’t be done, has been done,” the British government official said.

“Look at the language from the other European leaders today ... All the signals from them are that they are looking forward to continue to negotiate with the prime minister.”

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HURDLES

The EU is willing to start talks next month on a roughly two-year transition period to ease Britain out after March 2019 but wants more detail from London on what it wants before it will open trade negotiations from March.

The deal almost fell apart last week, when May’s Northern Irish allies rejected an initial agreement for fear that a promise to protect a free border with EU member Ireland could separate the region from the rest of the UK.

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After days of often fraught diplomacy, May rescued the deal to meet the EU’s requirements for “sufficient progress” but the last-minute wobble by the Democratic Unionist Party, which she depends on in parliament to get laws passed, and the defeat in parliament on Wednesday, underline the struggles she faces.

“I’m disappointed with the amendment,” she told reporters as she arrived at the summit. “But the EU withdrawal bill is making good progress through the House of Commons and we’re on course to deliver on Brexit.”

May’s success so far has won her some respite at home from political in-fighting between enthusiasts and sceptics of Brexit in her ruling party, and has reduced the prospect of a disorderly departure from the bloc.

At the summit, she was again keen to show that Britain was an active member of the bloc, committing to staying in the Erasmus university programme until the end of 2020 and taking part in discussions on the bloc’s plan for closer defence cooperation.

Over dinner, leaders also discussed responses to the migration crisis from Africa and the Middle East, and lingering deep divisions over how to share the load.

They confirmed a rollover of sanctions on Russia over the Ukraine crisis and reaffirmed their opposition to U.S. President Donald Trump’s move to recognise Jerusalem as the capital of Israel.