"We tell the criminals that we will not give up our right, no matter what the difficulties and obstacles are," Prime Minister Fuad Saniora told reporters after a three-hour Cabinet meeting.
"Our aim is to achieve justice and only justice. Without it — and without knowing the truth — the Lebanese will not rest and we cannot protect our democratic system and political freedom now or in the future," he said.
Rafik Hariri was killed along with 22 others in a massive suicide truck bombing in February 2005. The assassination sparked large anti-Syrian protests in Beirut, the Lebanese capital, and led to the withdrawal of Syrian troops from Lebanon, ending a 29-year military presence. Subsequent elections brought an anti-Syrian majority to power in parliament and the Cabinet.
The U.N. investigation has implicated top Syrian officials, but Syria has denied any role in the assassination.
Saniora, whose anti-Syrian majority dominates the Cabinet, convened the session Monday over President Emile Lahoud's objections and despite the resignations of six pro-Syrian ministers. Five of them, Shiite Muslims, quit in a dispute with the prime minister over their demand for more political share in decision-making.
But the resignations cast a shadow over the decision because Shiites were not represented in the Cabinet, contravening a provision in Lebanon's constitution to ensure the distribution of political power among Christian and Muslim sects.
Still, all 18 remaining ministers attending the meeting approved the United Nations document, and they defended the Cabinet's decision as legal.
"It is 100 percent constitutional," Information Minister Ghazi Aridi quoted Saniora as saying.
The government extended a hand to the opposition and those who have resigned, saying it was willing discuss their grievances.
"We have no choice but dialogue to agree on all the issues," Aridi said.
Earlier Monday, Environment Minister Yaacoub Sarraf resigned, joining five Shiite Muslim ministers who on Saturday quit the half-Christian, half-Muslim Cabinet.
"I don't see myself belonging to any constitutional authority in which an entire sect is absent," Sarraf said in his letter of resignation to Saniora. "So I am tendering my resignation from your government."
Sarraf, an independent who is allied with the pro-Syrian Lahoud and Hezbollah — a Shiite group listed by the United States as a terrorist organization — submitted his resignation only hours before the Cabinet met.
Lahoud had warned that the Western-backed Cabinet lost its legitimacy after the resignations of the Hezbollah and Amal ministers, citing Article Five of the constitution that states "all sects should be justly represented in the Cabinet."
Saniora swiftly rejected Sarraf's resignation as he did the other five.
With Sarraf's resignation, a quarter of the 24-member Cabinet had quit. His move makes it difficult for the Cabinet to govern, but legally it still has the necessary two-thirds quorum to meet and make decisions.
CBS News reporter Edward Yeranian reports that parliamentary leader Saad Hariri, a political ally of Saniora and the son of the assasinated prime minister, is accusing Hezbollah of an "attempted coup" in Lebanon over their withdraws from the government.
Yeranian says Hezbollah and its allies are planning large street demonstrations in Lebanon, but that no dates have been set.
The U.N. final draft, which the government received from the international body last Friday, sets in motion the process of creating a "tribunal with an international character" as authorized by the U.N. Security Council to try suspects in the bombing that transformed Lebanon.
President Lahoud had objected to some points in an earlier draft and declared it would not pass without his approval.
Lahoud's opposition toward convening the Cabinet to discuss the proposed tribunal sharpens the political divide in Lebanon between anti- and pro-Syrian forces; Lahoud and Hezbollah tilting toward Syria and Saniora and his allies opposing their powerful neighbor's influence over their country.
The anti-Syrian camp, which dominates the Cabinet, claims Syria is behind the opposition to the planned court that is envisioned to include Lebanese and foreign judges, to enable Syrian suspects to escape prosecution.
Saturday's withdrawal by the five ministers left the Shiites, the largest single sect in Lebanon, out of the government.
Sarraf's resignation strengthens the Shiites' bid for a larger presence in the Cabinet, now made up of Christians, Sunni Muslims and Druse in the Cabinet.
Pro-government politicians have been accusing Hezbollah of acting as "a state within a state," and of taking orders from Syria and Iran. Hezbollah increased its political clout during fighting with Israel in July and August.