The Iranian spokesperson further underlined that Tehran's principled policy is non-interference in the internal affairs of others.
Since Mr Hariri's surprise resignation last Saturday in a statement broadcast from a Saudi state-owned TV station in Riyadh he has not returned home, leaving the Lebanese asking: Where is our prime minister?
"My resignation came as a wake-up call for Lebanon", he said.
"I have resigned. I am going to Lebanon very soon and I will resign in a constitutional manner", he said in the first television interview after his resignation.
-Saudi Arabia announced Monday that the Saudi-led coalition fighting Shiite rebels in Yemen will begin reopening airports and seaports in the Arab world's poorest country, days after closing them over a rebel ballistic missile attack on Riyadh.
Aoun said he would not accept Hariri's resignation until he returns to Lebanon to explain his position. Although he met with various ambassadors in the Saudi capital of Riyadh in the days that followed, no one in Lebanon was really sure what was happening to him.
He added that a marathon planned in Beirut on Sunday in which tens of thousands are expected to participate should be "a national sports demonstration for solidarity with Prime Minister Hariri and his return to his country". He added that anything Hariri has said or may say "does not reflect reality" due to the mystery of his situation.
Meanwhile, the Arabic-language al-Joumhouria (The Republic) daily newspaper quoted Aoun as saying on Saturday that Beirut would refer Hariri's case to the UN Security Council within a week if his destiny remains unclear.
But Lebanese officials fear that during that meeting, Harari failed to take a hard enough stance against Hezbollah, the Shia Islamist group hated by Saudi Arabia - and included in Lebanon's coalition government.
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.
The cardinal had planned his visit before Hariri announced his resignation.
The Nov. 4 resignation triggered a political crisis in Lebanon, along with rumors about whether Hariri was under house arrest or being coerced to quit. Several sources believe that Saudi Arabia is holding Hariri against his will, a claim the kingdom has rejected.