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The meeting took place as senior U.S. and European officials arrived in Egypt to meet with the country’s military leaders.

U.S. Under Secretary of State for Political Affairs William J. Burns came Monday for a three-day visit that included a speech before the Arab League.

“We’ll continue to encourage concrete steps to build confidence and to sustain the momentum of the transition, ranging from the constitutional amendments that are being considered, through careful preparations for elections, to the further release of political detainees, to the lifting of the Emergency Law,” Mr. Burns said to the pan-Arab body.

The British prime minister met with Defense Minister Hussein Tantawi, Prime Minister Ahmed Shafiq and members of the country’s opposition groups.

He told reporters on the plane to Cairo that he would to “talk to those currently running Egypt to make sure this really is a genuine transition from military rule to civilian rule.”

Mr. Cameron told Mr. Tantawi, the head of the military council running the country, that Britain wanted to support Egypt’s transition to democracy. “As old friends of the Egyptian people, we come not to tell you how to do things, but to ask how we can help you do what we know you want to do,” he said.

Mr. Cameron said he would not meet with representatives of the Muslim Brotherhood, Egypt’s largest and best-organized opposition group, which was banned but tolerated under Mr. Mubarak.

The group announced Monday that it had chosen a name for its new political party, Freedom and Justice. Though allowed to compete in elections as independents, the Muslim Brotherhood was not allowed to turn itself formally into a political party under the previous regime.

Addressing recent anti-government protests around the region, Mr. Cameron called on Middle Eastern governments to respond with “reform, not repression.”

Libya’s response has been particularly brutal, and Mr. Cameron called its treatment of protesters “completely appalling and unacceptable.”