Hariri was appointed prime minister late past year.
Lebanese President Michel Aoun welcomed Hariri's statements and said he hoped the prime minister would return to Lebanon soon.
On Thursday, the State Department called for "unimpeded access" for humanitarian aid to Yemen, after Saudi Arabia imposed a blockade on the country to stem the flow of arms to Iran-aligned Houthi fighters.
Saudi Arabia announced it shut down all ports after a November 4 ballistic missile attack on Riyadh near its worldwide airport by the Houthis. Saudi Arabia has ordered its citizens to leave Lebanon post haste and has advised its people not to travel to the country from any other global destinations.
He spoke after pressure from Lebanese officials, who said his resignation was not accepted because it was declared in Saudi Arabia.
Hariri also accused Iran and the Lebanese resistance movement, Hezbollah, of meddling in the Arab countries' affairs; an allegation the two have rejected.
Tillerson's statement also urged "all parties both within Lebanon and outside" to respect Lebanon's independence and said there was no role for any foreign forces.
Trump tweeted on Monday that he had "great confidence in King Salman and the Crown Prince of Saudi Arabia" following the mass arrests - the biggest such purge of the kingdom's affluent elite in its modern history. The Houthis have denied that.
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Hariri's office said he met several diplomats in Riyadh on Monday including the British and German ambassadors.
The United States regularly criticizes Iran and Hezbollah for their role in Lebanon.
Tillerson told reporters the purge appeared "well intended" but the mass arrests, which have swept up officials long known in Washington, also fueled USA concerns.
"We are preoccupied by the situation in Lebanon. we are worried about its stability, we are worried about its integrity, we are worried about non-interference", Jean-Yves Le Drian said.
Many commentators consider the interview as another attempt by Riyadh to prove that Hariri is "free to move" in the Gulf Kingdom. He pleaded with the interviewer to finish the questioning and said he was "tired".
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.
Asked why Hariri has been in Saudi Arabia for so long, al-Mouallimi replied: "He has a house in Saudi Arabia". So it's not unusual that Saad Hariri is in Saudi Arabia.