BRUSSELS — David Davis, Britain’s secretary for exiting the European Union, resumed talks Monday over the rights of the European citizens in the UK as well as what financial payments Britain will have to make.

Davis discussed the issues with the EU’s chief negotiator, Michel Barnier. He left after three hours — leaving technical talks to a team of 98 British officials — and plans to return Thursday to see whether progress had been made on priorities identified by the bloc.

In an acknowledgment that last month’s opening of negotiations had achieved little, Davis said that it was crucial to now “get into the substance of the matter.’’

The rush to move talks forward comes as open divisions in the British Cabinet make it hard for European leaders to know what Britain wants.

Davis, a potential successor to Prime Minister Theresa May, is at the center of the political intrigue.

Davis is among the members of the Cabinet said to be unhappy about the prime minister’s policy toward the EU.

Bloomberg News