The Iranian foreign minister, Abbas Araghchi, held talks in Oman on Saturday with its top diplomat on safe passage in the Strait of Hormuz but made no public commitment to allow ships to freely pass through the critical waterway, despite a U.S. demand.

After meeting with the Omani foreign minister, Mr. Araghchi said the two men had discussed safe passage in the strait, a vital channel for global oil and gas, without elaborating. Iran blockaded the strait during the war with the United States and Israel, and it has yet to fully reopen despite the cease-fire signed last month.

The comments came after a heavy week of skirmishes between the United States and Iran focused on the strait. Adding to the tensions, President Trump and Iran’s supreme leader continued to trade threats into the weekend. In a rare written message on Saturday, Ayatollah Mojtaba Khamenei vowed revenge for the killing of his father and predecessor, Ayatollah Ali Khamenei, calling it the “demand of our nation.”

It is his first statement since a weeklong funeral for the elder Ayatollah Khamenei, culminating in his burial in Mashhad on Thursday. Although many Iranians loathed his repressive 37-year rule, millions joined processions across Iran and Iraq, which the Islamic republic used to project unity and defiance toward its enemies.

The ayatollah’s rhetoric deepened the uncertainty hanging over the fragile truce. While the Trump administration had said the cease-fire would fully lift Iran’s blockade of the Strait of Hormuz — which began after the U.S.-Israeli war on Iran in February — that has yet to be borne out.