LONDON — Prime Minister David Cameron will deliver his postponed address on Britain’s future relations with Europe on Wednesday, his office said Monday.

Mr. Cameron had planned to deliver the speech in Amsterdam on Friday but delayed it amid the Algerian hostage crisis, in which at least three Britons were killed. However, Mr. Cameron’s office released excerpts suggesting he had planned to explicitly warn that Britain might leave the European Union unless the bloc changed the way it was run.

Under pressure from his Conservative Party, Mr. Cameron has signaled his readiness for a referendum on the relationship with Europe, although the precise question to be asked is not clear.

The United States has been unusually public in its insistence that Britain, a close ally, stay in the union. Last week, a White House spokesman quoted President Obama as telling Mr. Cameron by telephone that “the United States values a strong U.K. in a strong European Union, which makes critical contributions to peace, prosperity and security in Europe and around the world.”