Iran’s top leader said Friday that trusting or cooperating with the United States would be a big mistake, an assertion that seemed to rule out any greater collaboration despite the nuclear deal reached nearly a year ago.

The statement by the leader, Ayatollah Ali Khamenei, made in a nationally televised speech, was the latest in a series of signals that Iran’s senior leadership was not likely to allow any easing of hostility toward the United States.

“We have many small and big enemies,” the ayatollah said, according to translated accounts of his speech in the Iranian media, noting that the worst are the United States, Britain and Israel, which he described as “the damned and cancerous Zionist regime.”

The backdrop for Mr. Khamenei’s speech was the 27th anniversary of the death of his predecessor, Ayatollah Ruhollah Khomeini, the founder of the Islamic revolution that overthrew the Western-backed shah of Iran in 1979.