The move was linked to a long-running dispute over the UN-backed Special Tribunal for Lebanon (STL), which is reportedly set to indict high-ranking Hezbollah operatives in the 2005 assassination of ex-premier Rafiq Hariri, Saad's father.
The resignations came after a Saudi-Syrian bid to defuse tensions over the tribunal failed to find a compromise between the two rival camps.
Analysts have predicted a drawn-out crisis that risks spiralling into more violence in the troubled Middle Eastern country.
In Washington, the Pentagon said the United States is keeping a close eye on the situation.
"We do know that political tension, unrest and especially any violence that might follow are threats to regional stability and security," spokesman David Lapan said.
"The US government desires that all parties use peaceful means to resolve the situation. We continue to monitor the situation very closely," Lapan said.
The United States, a major supplier of military aid to Lebanon, "has a valuable relationship with Lebanese armed forces and we're committed to do what we can to strengthen the sovereignty of the institutions as well as of the government of Lebanon."
For months, Hezbollah has been pressing Hariri to disavow the STL, which is reportedly set to indict senior members of the militant party.
The group has accused the tribunal of being part of a US-Israeli plot and has warned of grave repercussions should the court implicate any of its members.
Hariri, 40, has not commented on Wednesday's walkout, which was timed to coincide with his meeting US President Barak Obama in Washington.
He met French President Nicolas Sarkozy in Paris on Thursday and will see Turkish Prime Minister Recep Tayyip Erdogan in Ankara on Friday.
Hariri's pro-Western coalition has 60 seats while the Iranian-backed Hezbollah and its allies have 57.
Analysts said Druze leader Walid Jumblatt could play a key role in forming a new government.
Jumblatt, who holds 11 key votes in the 128-member parliament, could tip the scale. For years, he has been allied with Hariri, but he moved closer to the Shiite Hezbollah in 2009.
"It is too early to say what I will do," Jumblatt told AFP. "When the consultations on naming a new premier begin, we'll see."
A Hezbollah statement said Jumblatt met Hezbollah chief Hassan Nasrallah on Thursday.
Hezbollah's Al-Manar television said Nasrallah would address the "political developments in a speech soon," without elaborating.
An official close to the Hezbollah-led opposition said there was still a chance for the Saudi-Syrian initiative to succeed, in which case Hariri would easily be reappointed.
"If both sides agree to remain on that track, then no one can compete with Hariri," the official told AFP. "If they get off that track, then all options are open as far as other candidates for the premiership."
Hezbollah MP Mohammed Raad said the party would nominate for premiership a leader with "a history of resistance" but stopped short of giving names.
Hariri's bloc has ruled out the nomination of anyone other than the outgoing premier.
Neighbouring Israel slammed Hezbollah's walkout as an attempt to "blackmail" the international community and prevent the publication of the tribunal's indictments.
Iran in turn blamed the United States and Israel for the cabinet collapse, accusing them of "sabotage and obstruction."
The government crisis has sparked fears of a repeat of the events of May 2008, when an 18-month political crisis culminated in sectarian violence that brought the country close to civil war.
Late on Thursday two grenades were thrown at an office of Hezbollah ally the Free Patriotic Movement north of Beirut, a security official said. No casualties were reported.