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.

Iranian media said on Monday there were no negotiations between Tehran and Washington after US President Donald Trump announced talks towards ending the war.

"There are no talks between Tehran and Washington," said Mehr news agency citing Iran's foreign ministry, adding that Trump's statements were part of a push "to reduce energy prices".

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's powerful parliament speaker Mohammad Bagher Ghalibaf threatened on Sunday to irreversibly destroy vital infrastructure across the region if the United States and Israel attacked its own.

Israeli Prime Minister Benjamin Netanyahu vowed on Sunday to pursue senior commanders of Iran's Revolutionary Guards "personally", during a visit to an Israeli town struck by an Iranian missile the previous day.

Iranian missile strikes on two southern Israeli towns wounded more than 100 people on Saturday, medics said, after Israeli air defence systems failed to intercept the projectiles.

Benjamin Netanyahu must soon decide when to hold Israel’s next elections. With war raging on multiple fronts and no end in sight, Israel’s enemies in Iran and Lebanon may help make that decision for him.

After three weeks of war, the Trump administration has begun initial discussions on the next phase and what peace talks with Iran might look like, a U.S. official and a source with knowledge told U.S. news portal Axios.

Trump said Friday that he was considering "winding down" the war, though U.S. officials said the expectation was there would still be two to three additional weeks of fighting. In the meantime, Trump's advisers want to start laying groundwork for diplomacy.