In a televised interview with Future Television's Paula Yacoubian, Saad Al Hariri re-confirmed his resignation from his position as Lebanon's Prime Minister.
In a television interview, the Saudi-allied Hariri held out the possibility he could yet rescind his resignation if Hezbollah agreed to stay out of regional conflicts such as Yemen, his first public comments since he read out his resignation on television from Riyadh eight days ago.
When he resigned on November 4, he said he feared assassination.
Lebanon sits on the Levant Basin in the eastern Mediterranean where a number of big subsea gas fields have been discovered since 2009, including the Leviathan and Tamar fields.
White House Press Secretary Sarah Huckabee Sanders said in a statement on Saturday that Washington calls upon "all states and parties to respect Lebanon's sovereignty, independence, and constitutional processes".
But he said his resignation was his decision, dismissing reports he was forced to quit a unity government with Hezbollah.
On Friday, a spokesman for France's foreign ministry said: "We wish Mr Saad Hariri to have all his freedom of movement and to be fully able to play the essential role that is his in Lebanon".
He also repeatedly said he was ready to die for Lebanon - his father, former Prime Minister Rafik Hariri, was killed by a auto bomb in Beirut in 2005 - but added that he didn't want his children to go through that kind of ordeal.
Hariri also accused Iran and Hezbollah of sowing strife in the Arab world. He singled out Yemen, where Saudi-led Arab forces are fighting against the Houthi movement which Riyadh says is backed by Iran. Aoun has been convening high-level meetings with Lebanese politicians and foreign diplomats since Hariri stepped down.
"There was a danger in Lebanon and I wanted to take additional steps and send a positive shock". A Saudi-led coalition has been at war with the Houthis since March 2015.
Earlier Sunday, thousands of people attending Lebanon's annual marathon used the event to urge Hariri to return home.
Lebanon's president said Mr Hariri was being held against his will in Saudi Arabia.
Hariri was a regular participant in the marathon, giving the worldwide sports event a big boost.
While Mr Hariri's speech may have been encouraging in so far as offering a way out of Lebanon's current political crisis, many observers remarked that he still appeared to be more a mouthpiece for Saudi policy rather than someone speaking on his own behalf.
One woman raised a placard reading: "We want our prime minister back".
In the northern city of Tripoli on Saturday, unknown assailants burned posters of Saudi Crown Prince Mohammed bin Salman in a sign of the rising tensions.