But the government has a solid majority in the 128-member parliament and is unlikely to lose a no-confidence vote despite unprecedented public protests since Hariri's death on February 14.
"It will be the end of every deputy who gives confidence in ministers who incited, covered or remained silent and are not really investigating this crime," said Druze opposition MP Marwan Hamadeh, who survived an attempt on his life in October.
"The government has already fallen: the people toppled it, developments felled it," he told local LBC television.
Thousands of Lebanese demonstrated in Beirut on Monday, calling for the government to resign and Syria to pull out its 14,000 troops from Lebanon, while the United States and France piled up international pressure on Damascus.
US President George W. Bush, speaking at the start of a trip to Europe, branded Syria, which has denied any involvement in the bomb blast that killed Hariri, an "oppressive neighbour" to Lebanon and insisted Damascus must "end its occupation".
Later, Bush and French President Jacques Chirac issued a joint call for a Lebanon "free from foreign domination".
Bush and Chirac, whose country formerly ruled both Lebanon and Syria, condemned Hariri's killing. Their joint statement did not blame Syria but backed a UN investigation into the attack.
The European Union called for an international probe into Hariri's death and underlined its support for a United Nations resolution calling for Syria to withdraw.
But Saudi Arabian Foreign Minister Prince Saud al-Faisal said calls for an international probe were premature and Beirut should be allowed to hold its own investigation.
He said in remarks published on Tuesday that countries should not rush to accuse Syria of involvement in the killing.
"We cannot accuse one side before we know the facts," the London-based Asharq al-Awsat daily quoted him as saying. "Those who accuse Syria without evidence will be open to criticism."
Hariri, who holds Saudi citizenship, had close business, political and personal ties to the Saudi royal family. He was also an ally of Syria for much of his dozen years in and out of power, finally quitting in October after Damascus insisted on extending the term of his rival President Emile Lahoud.
Syria indicated on Monday it would start withdrawing some of its troops from Lebanon soon in line with the Taif Accord which ended Lebanon's 1975-90 civil war.
Police raised the death toll from the bombing that devastated Hariri's motorcade in Beirut to 18 dead with one missing. More than 135 people were wounded.
Parliament Speaker Nabih Berri agreed on Monday to opposition demands to hold a special session on February 28 to question the government over the assassination.
Opposition MPs had demanded that parliament suspend debate on a key law organising general elections due by May until the authorities say who killed Hariri.
Berri said next week's session would be "the start of a real dialogue" between the government and the opposition - though the opposition wants talks with Syria, not its local allies.
Berri said parliament would pass the electoral law early next month. Both government and opposition say they want polls held on time.