U.S. President Donald Trump speaks during a cabinet meeting in the Cabinet Room of the White House in Washington on May 27. [AFP/YONHAP]

U.S. President Donald Trump said Wednesday that his administration is "not satisfied" yet, though Iran is "very much intent" on reaching a deal with the United States to end hostilities, amid reports that the two countries are inching toward a peace agreement.

Speaking at a Cabinet meeting, Trump also stressed that "nobody" will control the Strait of Hormuz, rejecting Iran's push to regulate traffic through the crucial waterway, while saying that his administration is not discussing sanctions relief in negotiations with Tehran.

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His remarks came as Washington and Tehran are working to narrow their differences on a memorandum of understanding that reports say would extend their cease-fire, reopen the Strait of Hormuz and continue negotiations on Iran's nuclear program.