The Conservative leader will use the meeting in Brussels to update EU counterparts on her plan to start formal exit talks by the end of March, paving the way for Britain to leave the bloc by early 2019.
But as she arrived to take the seat formerly occupied by David Cameron, she made clear Brexit was not the only issue on the table, calling for a "robust and united" EU response to Russia's "atrocities" in Syria.
May was excluded from last month's summit of 27 leaders in Bratislava, but EU president Donald Tusk played down speculation that the two day meeting in Brussels would be a frosty affair.
"Some media described her first meeting in the European Council as entering the lion's den. It's not true. It's more like a nest of doves," he told reporters.
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"She'll be absolutely safe with us. And I hope that she will also realise that the European Union is simply the best company in the world."
May's plan to trigger Article 50 by March, unveiled at her party conference earlier this month, has been welcomed by European leaders who had been pressing for a swift divorce.
But she angered many member states by stating her intention to limit EU migration into Britain, while also seeking "maximum freedom" to operate in the EU's single market.
European leaders have repeatedly said the two demands are incompatible, and warned London should expect to pay a heavy price for its decision to leave.
Over a working dinner today evening, May will urge EU leaders to help make Brexit work for both sides, a source in her office said, speaking on condition of anonymity.
"We want our departure to be a smooth, constructive, orderly process, minimising uncertainty," the source said.
After the summit ends tomorrow, May will hold her first bilateral talks with European Commission chief Jean-Claude Juncker, over lunch.
His spokeswoman said it would be an "introductory" meeting with no talk of Brexit.