The administration, using a secret communications channel officials would not describe, warned Iranian Supreme Leader Ayatollah Ali Khamenei that closing the narrow, strategically important strait between the Gulf of Oman and the Persian Gulf would be considered crossing a "red line" that would not be tolerated, the officials told The New York Times.
The officials would not say if Khamenei or any other Iranian official had replied to the unusual contact between the two countries, the Times said.
Senior Obama administration officials have publicly said Iran would cross a red line if it made good on recent threats to close the strait, which 16 million barrels of oil -- about a fifth of the world's daily oil trade -- flow through every day.
"They need to know that if they take that step, they're going to get stopped," Defense Secretary Leon Panetta said on the CBS News program "Face the Nation" Sunday.
Joint Chiefs of Staff Chairman Gen. Martin Dempsey said on the same program Washington would "take action and reopen the strait," which the Times said could be accomplished only by military means, including minesweepers, warship escorts and possible airstrikes.
Administration officials and Iran analysts have said they believe Iran's threats, coming amid antagonism over its nuclear program and the possibility of increased Western sanctions, were swaggering efforts to intimidate and drive up oil prices.
But Dempsey told CBS Sunday Iran has the military capability to close the strait.
"The simple answer is yes, they can block it," he said, calling such a move "an intolerable act" that "we would take action and reopen."
The navy of Iran's 125,000-troop-strong Revolutionary Guard, a branch of Iran's military founded after the 1979 Iranian revolution, is the primary Iranian force controlling the strait and Persian Gulf.
The guard's navy has fast-attack speedboats and uses guerrilla tactics, in contrast with Iran's traditional state navy -- made up of aging big ships dating from Iran's monarchy under Shah Mohammed Reza Pahlavi -- the Times said.