CAIRO — In the highest-level American visit here since the Egyptian military removed the country’s first democratically elected president from power, Secretary of State John Kerry pressed Egyptian leaders on Sunday to stick to their “road map” for restoring democracy.

In substance as well as tone, Mr. Kerry’s visit to Egypt reflected the Obama administration’s determination to work with a military leadership that ruthlessly put down protesters from the Muslim Brotherhood, the Islamist movement that put forth the successful candidacy of President Mohamed Morsi, who was ousted on July 3. A military government, now firmly entrenched here, has promised to establish a civilian-led government.

“The road map is being carried out to the best of our perception,” Mr. Kerry said, referring to the plan by the Egyptian authorities to conduct a national referendum on an amended Constitution and hold parliamentary and presidential elections by next spring.

“There are questions we have here and there about one thing or another,” he added in a joint news conference with his Egyptian counterpart. “I think it’s important for all of us, until proven otherwise, to accept that this is the track Egypt is on and to work to help it to be able to achieve that.”