The Lebanese government held a meeting on Monday to consider the UN-drafted framework to set up a tribunal to try suspects in the 2005 assassination of former Prime Minister Rafik al-Hariri.
As he arrived at the meeting in Beirut, Lebanese Defence Minister Elias El-Murr said he supported an international tribunal, "which will stop the accumulations of crimes in this country which the Lebanese have paid its price for years."
Western-backed Lebanese Prime Minister Fuad Saniora insisted on holding the meeting, despite the resignation of six pro-Syrian ministers and opposition from President Emile Lahoud.
Environment Minister Yaacoub Sarraf, a Christian Cabinet minister allied with Hezbollah, resigned on Monday.
Sarraf joins five Shiite Muslim ministers who quit the half-Christian, half-Muslim Cabinet on Saturday.
The 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, which is now made up of Christians, Sunni Muslims and Druse.
It also reduces the sectarian nature of the dispute.
Hezbollah recently threatened to call mass protests on November 13 with the aim of bringing down the government, unless the Shiites obtained one-third of Cabinet portfolios plus one.
That would effectively give them veto power because Cabinet decisions require approval by two-thirds of ministers.
Hezbollah has since said that it would not necessarily call protests immediately and that other steps could be taken first, though it did give specifics on the actions it might take.
Sarraf pulled out of the government as the country was already on the verge of a showdown between pro- and anti- Syrian forces.
The resignations come after talks on a national unity government failed to reach agreement.
Pro-government politicians have been accusing Hezbollah, which gained increasing political clout for its fierce fight against Israel in July and August, of acting as "a state within a state," and of acting on behalf of Syria and Iran.