The Western-backed premier, who returned to Lebanon on Friday from week-long talks in the United States, France and Turkey, said the collapse of his 30-member cabinet was "unprecedented in the history of Lebanese governments."
Hariri's statement came two days after the powerful Iranian-backed Hezbollah and its allies resigned from the cabinet in a dispute over a UN-backed probe into the 2005 murder of his father, ex-premier Rafiq Hariri.
Hezbollah, Lebanon's most powerful armed faction, for months has been pressuring Hariri to reject the STL, which is reportedly poised to indict high-ranking members of the Iranian-backed party in the Hariri assassination.
The Shiite group has warned of grave repercussions should it be accused of the murder.
Although he did not specifically refer to the tribunal, Hariri on Friday made clear he would not cave in to pressure to reject the court.
He accused Hezbollah of refusing to make concessions while pressing him to "make personal and national sacrifices."
Hariri said his consultations this week with US, Saudi, French and Turkish officials were aimed at "protecting Lebanon from sliding into the unknown."
"Some took advantage of the situation to ... put an end to the political truce" brokered by Saudi Arabia and Syria, he said, adding that dialogue was the only way out of the current impasse.
"No one party in Lebanon can rule on its own," he said.
Sleiman, who declared the government a caretaker cabinet after Wednesday's resignations, on Monday is to begin consultations with MPs on appointing a new premier.
Turkey and France have been leading the way in efforts to prevent an outbreak of violence in the troubled Middle Eastern country.
France, Lebanon's former colonial power, has proposed the creation of an international "contact group" similar to that of Bosnia in the 1990s to negotiate a settlement, a European diplomat in Beirut told AFP.
"The contact group would include Syria, Saudi Arabia, France, the United States, Qatar, Turkey and possibly other countries," the diplomat said on condition of anonymity.
The French foreign ministry refused to confirm or deny the proposal.
Turkey, a NATO member seeking to position itself as a key broker in the Middle East, has said it was ready to play "an active role" in helping end the crisis in Lebanon.
Turkish Prime Minister Recep Tayyip Erdogan said earlier on Friday after meeting with Hariri that he was ready to contact regional heavyweights Syria and Iran among others, Turkey's Anatolia news agency reported.
And the US ambassador to Lebanon, Maura Connelly, reiterated her country's unwavering support for the tribunal, urging Lebanon's feuding camps to exercise restraint.
The STL "is an irrevocable, international judicial process; its work is not a matter of politics but of law," Connelly said. "The resignation of some of Lebanon's ministers will not change this."
Druze leader Walid Jumblatt, whose parliamentary bloc will be the first to meet with Sleiman on Monday, controls 11 key votes in parliament that could make or break the next government.
Jumblatt had been allied with Hariri but moved closer to Hezbollah in 2009.
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