May had breakfast with Dutch Prime Minister Mark Rutte in The Hague before heading to Berlin for lunch with Chancellor Angela Merkel, and was then to travel on to Brussels, AFP reported.
She is seeking "reassurances" over provisions in the EU withdrawal agreement concerning Northern Ireland, which she hopes could persuade her rebellious Conservative party to support it.
European Commission chief Jean-Claude Juncker said ahead of meeting May that he was "surprised" at being asked for more talks.
I'm surprised because we had reached an agreement on November 25" at the last EU summit, he told the European Parliament in Strasbourg.
"The deal we have achieved is the best deal possible, it's the only deal possible.
"There is no room whatsoever for renegotiation but of course there is room, if used intelligently, to give further clarification and further interpretations."
MPs in the House of Commons were due to vote on the deal on Tuesday night, but May deferred it on Monday, admitting she expected to lose by a "significant margin".
Her spokesman said Tuesday the vote would be rescheduled before January 21 -- just months before Britain leaves the EU on March 29.
EU President Donald Tusk, who was also to meet May in Brussels, has called a meeting of the other 27 EU leaders on Thursday to discuss the latest Brexit developments.
They and May were already due to attend a European Council summit on Thursday and Friday, which the British prime minister is expected to use to further press her case.
Irish Foreign Minister Simon Coveney said his government ruled out changes to the wording of the withdrawal agreement, but said there could be "a political declaration coming from a European Council".
"The Irish government doesn't have an issue with providing reassurance if that's helpful," he told national broadcaster RTE.
May faces strong opposition from her own Conservative MPs and parliamentary allies over a clause in the Brexit deal designed to keep open the border with Ireland.
The so-called backstop risks tying Britain into a customs union with the EU for years after it leaves the bloc – far from the clean break that eurosceptics want.
"I have heard those concerns and I will now do everything I possibly can to secure further assurances," May told mutinous MPs on Monday, after pulling the vote. But it is far from clear what she can achieve.
One of her ministers, Martin Callanan, said in Brussels on Tuesday that Britain is seeking "additional legal reassurances that UK cannot be permanently trapped in the Irish backstop".
Leader of the House Andrea Leadsom said this could take the form of "an addendum".
May said on Monday that "nothing should be off the table", but warned that reopening the withdrawal agreement could see other countries seek to remove bits they do not like, for example on fishing rights.