MANILA — Secretary of State John Kerry said here on Tuesday that the United States would give the Philippines $40 million in maritime security assistance and was negotiating with Manila to rotate more American military forces through the country, the latest signs of the Obama administration’s concerns about mounting pressure from China on its neighbors.

Both steps have been months in preparation, and Mr. Kerry took pains not to portray them as direct responses to the most recent difficulties in Chinese-American relations. Even so, they signal that the United States may not back down quickly as China becomes increasingly assertive in claiming islands, airspace and large expanses of ocean in the East China Sea and South China Sea.

“The United States strongly opposes the use of intimidation, coercion or aggression to advance territorial claims,” Mr. Kerry said. “The United States remains firmly committed to the security of the Philippines and the region.”

Appearing at a joint news conference after an afternoon of discussions, Mr. Kerry and the Philippine foreign secretary, Albert F. del Rosario, strongly criticized China’s recent unilateral declaration of an air defense identification zone over the East China Sea, including airspace previously monitored mainly by Japan and South Korea.