The U.N.-backed Special Tribunal for Lebanon is investigating the 2005 assassination of Hariri, a former prime minister. This summer, it named four members of Hezbollah as the likely perpetrators of the assassination.
The March 14 alliance, which led the previous Lebanese government under Saad Hariri, the slain prime minister's son, said the tribunal was vital for the country.
"The Special Tribunal for Lebanon is the cornerstone for Lebanon's civil peace and the rise of a state capable of implementing the law equally among all citizens," it said in a statement published by Lebanese news outlet Naharnet.
Lebanese leaders in the government of Prime Minister Najib Mikati stressed support for the tribunal, though March 14 said it would be better if Beirut handed suspects over to tribunal authorities.
Lebanese authorities in their August update to the tribunal said they weren't able to apprehend any of the suspects named by the tribunal.
Hezbollah leaders said the case is part of an Israeli ploy to discredit the Shiite resistance. Lebanese President Michel Suleiman, addressing the U.N. General Assembly last week, said Beirut "has always been committed" to respecting the tribunal.