Hezbollah chief Sheikh Hassan Nasrallah said his group would not support Sa'ad Hariri as interim prime minister while a new government is being formed.
Last Wednesday, Hezbollah and its allies resigned from Lebanon's unity government, causing the coalition to collapse.
"The opposition unanimously will not name Hariri tomorrow," Nasrallah said over the weekend. "It was a must to topple the incapable government because bringing it down might - and I say might - open the door for Lebanon to form a loyal government," he said.
Nasrallah defended the group's decision, calling the move "constitutional, legal and democratic."
At the request of Lebanese President Michel Suleiman, Hariri agreed to stay on as the transitory government's acting prime minister until a new coalition is formed.
Hezbollah has been demanding that the government reject the findings of the U.N.-sponsored Special Tribunal on Lebanon investigating the 2005 assassination of Sa'ad's father, former Prime Minister Rafik Hariri.
The tribunal is expected to present evidence of its three-year investigation this week and issue indictments for members of Hezbollah.
Hezbollah has long denied any responsibility for Hariri's assassination, labeling the U.N. tribunal "an Israeli tool."
Meanwhile following a meeting with Hariri on Sunday, U.S. Ambassador to Lebanon Maura Connelly called the tribunal an "independent, international judicial process...not subject to political influence, either from inside Lebanon or from outside."
"The efforts by the Hezbollah-led coalition to collapse the Lebanese government only demonstrate their own fear and determination to undermine Lebanon's sovereignty and independence," she said.
Hariri invited Hezbollah to join a unity coalition 14 months ago, granting the group parliamentary veto power.
Suleiman will begin consultations with parliamentarians on Monday before nominating a new prime minister.
Reuters contributed to this report.