The New York Times is quoting unnamed U.S. officials as saying Washington has sent a message to Iran's Supreme Leader, Ayatollah Khamenei, that closing the Strait of Hormuz would provoke a U.S. response.
The report published late Thursday said the covert message was not delivered through the the Swiss government, the usual way Washington communicates with Iranian leaders.
Iran recently threatened to close the narrow waterway, a vital shipping route for the global oil trade. U.S. Secretary of State Hillary Clinton said earlier this week that the threat is "provocative and dangerous."
U.S.-Iran tensions are also high over the assassination of a top Iranian nuclear scientist in a bomb attack in Tehran Wednesday. Iran blames the United States and Israel and is demanding the U.N. Security Council condemn the murder.
Israel and the United States deny involvement. But U.S. Defense Secretary Leon Panetta said Thursday U.S. officials have some ideas who may be responsible.
Western nations have been stepping up pressure on Iran to end its nuclear enrichment program, which they say is part of a drive to develop nuclear weapons. Iran insists its nuclear program is entirely peaceful.
Some information for this report was provided by AP, AFP and Reuters.