U.S. President Donald Trump said Tuesday that Iran gave him a "very big present" related to the Strait of Hormuz, boosting his confidence that he was talking to the right people in Tehran to end the war.

The U.S. and a group of regional mediators are discussing the possibility of holding high-level peace talks with Iran as soon as Thursday, but are still waiting for a response from Tehran, two sources with knowledge of the discussions told U.S. news portal Axios.

U.S. President Donald Trump told reporters on Monday that his envoys held talks with a senior official in the Iranian leadership and claimed the parties are in agreement on many points.

Trump walked back his threat to strike Iran's power plants on Monday, citing productive negotiations.

President Donald Trump said Monday that there are "major points of agreement" in U.S.-Iran talks which he said must result in Tehran giving up its nuclear ambitions and enriched uranium stockpile.

President Donald Trump has extended his deadline for Iran to reopen the Strait of Hormuz, saying the U.S. will hold off on power plant strikes for five days.

Trump made the announcement on his Truth Social site Monday, hours ahead of a deadline later in the day.

Iran's military threatened on Sunday to completely shut down the strategic Strait of Hormuz if U.S. President Donald Trump acts on threats to target the country's power plants.

U.S. President Donald Trump on Saturday gave Iran 48 hours to reopen the Strait of Hormuz to shipping or face the destruction of its energy infrastructure, as Tehran launched its most destructive attack yet on Israel.

Iran recently fired two ballistic missiles toward the joint U.S.-UK military base at Diego Garcia in the Indian Ocean, The Wall Street Journal reported Friday, citing U.S. officials.

The United States and Israel struck Iran's Natanz nuclear facility on Saturday, the Islamic republic's atomic energy organization said.

U.S. President Donald Trump said Friday that he was considering "winding down" military operations against Iran, as the United States temporarily eased sanctions on Iranian oil shipments to stem a global supply crisis.

Iran launched a new wave of drone and missile attacks on Saudi Arabia and Israel meanwhile after supreme leader Mojtaba Khamenei claimed to have dealt a "dizzying blow" to his country's enemies.