Leaders from the United States and Iran painted a positive but cautious picture of talks between the nations over Iran’s nuclear program Saturday, after the third phase of the discussions wrapped up in Oman.

The United States and Iran on Saturday concluded their third round of "indirect" nuclear talks mediated by host Oman with both sides seeing progress in reaching a deal.

The third round of talks in three weeks raised hopes for an Iran nuclear accord, which could avert a new Mideast conflict. President Trump said he believed a deal was within reach.

Trump says he favors a nuclear deal with Iran but won’t hesitate to take military action if talks collapse, insisting he won’t be dragged into war by Israel — but might enter one by choice.

U.S. President Donald Trump this week said he is open to meeting Iran's supreme leader or president and that he thinks the two countries will strike a new deal on Tehran's disputed nuclear programme.

US President Donald Trump's renewed threat comes as Washington and Tehran continue talks over the Iran's nuclear program, with a third round slated for Saturday in Oman.