The prime minister is seeking legally binding pledges from EU leaders on the Irish backstop - a key obstacle for MPs who oppose her Brexit deal.
The EU will not renegotiate the deal but may be willing to give greater assurances on the temporary nature of the backstop, the BBC understands.
The PM won the ballot on her leadership by 200 votes to 117 on Wednesday night.
The secret ballot was triggered by 48 of her MPs angry at her Brexit policy, which they say betrays the 2016 referendum result.
Speaking in Downing Street after the vote, Mrs May vowed to deliver the Brexit "people voted for" but said she had listened to the concerns of MPs who voted against her.
"I have heard what the House of Commons said about the Northern Ireland backstop and, when I go to the European council tomorrow, I will be seeking legal and political assurances that will assuage the concerns that members of parliament have on that issue," she said.