LONDON — Seeking to end a stalemate in negotiations over her country’s withdrawal from the European Union, Prime Minister Theresa May of Britain offered Friday substantial payments to the bloc during a two-year transition period immediately after the country’s exit.

Mrs. May’s long-awaited intervention, during a speech in Florence, Italy, was being watched closely in capitals on the Continent and in London, where members of her cabinet have been fiercely divided over Britain’s tortuous divorce from the bloc. The speech aimed to open the way to serious negotiations on what is commonly known as Brexit, and to a broader and more productive discussion about Britain’s relationship with the bloc.

However, while offering some concessions designed to do that, Mrs. May did not give any fresh insight into the type of ties she ultimately wants Britain to have to the bloc — a question that divides her cabinet and her Conservative, or Tory, Party.

The European Union’s chief negotiator, Michel Barnier, issued a cautious response, saying in a statement that, “We look forward to the United Kingdom’s negotiators explaining the concrete implications of Prime Minister Theresa May’s speech. Our ambition is to find a rapid agreement on the conditions of the United Kingdom’s orderly withdrawal, as well as on a possible transition period.”