MANAMA, BAHRAIN, AUG. 29 -- Iran said today that the United States had sent two recent messages expressing a desire to reestablish diplomatic relations with Tehran.

But Hojatoleslam Ali Akbar Hashemi Rafsanjani, the powerful speaker of Iran's Parliament, added that his government saw "no good intentions on the part of the United States" in the messages.

Rafsanjani, whose statements were reported by Iran's official news agency IRNA, also declared that Iran's relations with the Soviet Union have experienced "great developments" in recent weeks.

In Washington, State Department spokesman Rudi Boone said that he was unaware of any reports of overtures to Iran by the United States and could not confirm Rafsanjani's statement.

Rafsanjani's report of the two messages represented the first suggestion that the United States was making overtures to Iran since he disclosed last October that President Reagan had sent his former national security adviser, Robert C. McFarlane, to Tehran in an effort to improve relations with Iran.

That disclosure came amid reports that White House officials had shipped arms to Iran and diverted Iranian payments to the U.S.-backed rebels fighting the government in Nicaragua.

Secretary of State George P. Shultz acknowledged at a news conference Aug. 6 that the governments of the United States and Iran regularly communicate with each other through intermediaries.

Rafsanjani suggested that the United States should show its good intentions by freeing Iranian assets in the United States. These claims center on $11 billion in military equipment that was ordered by Iran before the fall of Shah Mohammed Reza Pahlavi but either was not delivered or was rejected by revolutionary Iran as shoddy merchandise.

Rafsanjani, appearing more conciliatory than any other Iranian leader has toward the United States in recent months, was quoted as saying, "If our relations are changed from hostility to friendly ties, many things may be changed."