By Noah Barkin and Elizabeth Piper

BRUSSELS (Reuters) - Arriving at her first European Union summit, Prime Minister Theresa May promised that Britain would remain a strong partner to the EU after Brexit and called for unity in pressuring Russia for its "sickening atrocities" in Syria.

May, who replaced David Cameron in July after Britons shocked the EU by voting to leave the bloc, was due to spell out her vision for Brexit at a dinner with her 27 counterparts on Thursday evening.

Her speech at a conference of her Conservatives in Birmingham in early October suggested she is leaning toward a so-called "hard Brexit" in which Britain would place limits on immigration and lose access to Europe's lucrative single market.

In the past weeks however, May and her ministers have sent out different signals, deepening the sense of confusion in other European capitals about her intentions and raising the pressure on May to spell out what she wants.

"This is my first European Council and I'm here with a very clear message: The UK is leaving the EU but we will continue to play a full role until we leave and we'll be a strong and dependable partner after we have left," she told reporters upon arrival.

Above all, she said it was important that the EU stand together in the face of Russian aggression in Syria. In the past weeks, Syrian government and Russian forces have stepped up air strikes on besieged rebel-held parts of the Syrian city of Aleppo, killing hundreds of civilians.

"It's vital that we work together to continue to put pressure on Russia to stop its appalling atrocities, its sickening atrocities in Syria," May said.

Leaders were due on Thursday to discuss the state of the bloc's deals with African countries to limit EU-bound migration from their territories, before turning to the topic of Russia over dinner and to economic issues, including a pending trade deal between the EU and Canada, on Friday.

But the meeting in Brussels may be overshadowed by Brexit. May has said she will trigger Article 50 of the EU treaty, which would start a two-year countdown to Britain's exit, by the end of March.

"NEST OF DOVES"

She has also made clear she would like to hold preparatory talks with EU governments before taking that step. But the EU has stuck firmly to its line, first spelled out in June in the aftermath of the British referendum, that there will be no early negotiations before Article 50 is invoked.

European Parliament President Martin Schulz, speaking to reporters as the leaders arrived, reiterated that stance, saying the EU would be "running into a trap" if it began substantive talks with Britain before London had formally notified its partners in writing that it intends to leave.

In London, May's Brexit minister, David Davis, told lawmakers that the government would do "anything necessary" to ensure the stability of the financial sector during the Brexit talks.

Banks in the City of London are worried that they could lose their right to sell services across Europe if May insists on curbing migration under a deal with the EU-27. If Britain places limits on free movement, it will lose its access to the single market, governments on the continent have warned.

European Council President Donald Tusk dismissed the chances of any real clash between May and other leaders in Brussels.

"Some media described her first meeting in the European Council as entering the lion's den," he said. "It is not true. It is more like a nest of doves - just look at me!"

German Chancellor Angela Merkel also played down the Brexit issue, saying she did not expect that discussion, which is due to take place at the end of the dinner, to last long.

Like May, she urged the summit to send a clear message to Russia about the "inhuman" bombings in Aleppo.

Merkel hosted Vladimir Putin in Berlin on the eve of the summit and, together with French President Francois Hollande, pressed the Russian leader to extend a pause in air strikes. Hollande referred to the attacks on the civilian population as "war crimes".

"I hope that the European Council can firm up our view that what is happening with Russian support in Aleppo is completely inhuman with regards to the inhabitants of Aleppo," Merkel said. "That is why there has to be work on a truce and not just one of a few hours followed by several hours of bombing but a permanent truce."

(Additional reporting by Alastair Macdonald, Francesco Guarascio, Philip Blenkinsop, Robert-Jan Bartunek and Jan Strupczewski in Brussels; editing by Mark Heinrich)