Lebanon's unity government collapsed last week when ministers loyal to Hezbollah quit their posts.
The dispute centered on a U.N.-backed tribunal's investigation into the 2005 assassination of Hariri's father, former Prime Minister Rafik Hariri. The tribunal is widely expected to blame Hezbollah for the killing.
Lebanese President Michel Suleiman asked Hariri to stay on as caretaker prime minister.
"This is a historic crisis that has touched all Lebanese," Hariri said Thursday. "We must resort to the constitution and constitutional organizations. This should be the basis on which everybody works."
The leaders of Turkey, Syria and Qatar met personally earlier in the week to approve the Turkey-Qatar mission to try to resolve the political crisis and the Turkish and Qatari foreign ministers were in Beirut this week for talks with Lebanese leaders.
"Due to some reservations they decided to stop their efforts in Lebanon at this time and leave Beirut for more consultations with their leaderships," according to a statement reported by Lebanese and Qatari news agencies.
"The United States supports the independence and sovereignty of Lebanon and believes that, ultimately, any decision will have to be made by the Lebanese people," U.S. Secretary of State Hillary Clinton said Thursday. "Any mediation effort engaged in by anyone outside of Lebanon itself should be aimed at supporting the people of Lebanon and making decisions that will lead to stability and security, justice, and a commitment to bringing those who committed the murders of Prime Minister Hariri and 22 others to account."
