Following the cabinet vote, the UN tribunal needs Lebanese parliamentary and presidential approval before it can go ahead.
The meeting was delayed due to concerns raised by pro-Syrian politicians, most of them Shia, who recently quit the cabinet.
A ministerial envoy held talks with Nabih Berri, the pro-Syrian parliament speaker, who had dismissed the meeting as unconstitutional.
Berri is also the head of Amal, a Shia group with ties to Hezbollah. Hezbollah has close links to Syria, which has been accused of involvement in the killing.
Berri had warned ministers that they could only convene on an emergency basis with the blessing of Emile Lahoud, Lebanon's president and a fellow Damascus ally.
"The solution lies in Mr Berri's hands," Marwan Hamadeh, the telecommunications minister, said as he left the speaker's residence after his talks.
The cabinet is determined to press ahead with the international court blueprint endorsed by the UN Security Council, endorsed shortly after the killing of Pierre Gemayel, a Maronite Christian politician who was critical of Syrian influence in Lebanon.
"...I am ready to postpone the cabinet meeting for a few days if there is a genuine willingness to discuss it"
Fouad Siniora, Lebanon Prime Minister
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Fouad Siniora, Lebanon's pro-Western prime minister, had offered to postpone the planned meeting for a few days. However, he demanded that Amal and Hezbollah first show a "genuine willingness" to advance the ratification of the court.
He said: "Since Hezbollah and Amal clearly indicated in an unequivocal manner that they are in favour of the formation of an international court to unmask the truth about the assassination of Rafiq Hariri and other crimes, I am ready to postpone the cabinet meeting for a few days if there is a genuine willingness to discuss it."
Supporters of Siniora allege that Hezbollah and Amal pulled out of the cabinet at the behest of their Syrian ally, which has been implicated in al-Hariri's murder by a UN inquiry and has voiced opposition to the international court.
The two Shia parties insist they left the cabinet in protest at the failure of cross-party talks to agree to their demands for a government of national unity including an allied faction in opposition since last summer's elections.
Earlier on Saturday, Samir Geagea, a Christian leader, said efforts to derail the tribunal could lead to more assassination bids against parliament members.
Geagea, a former militia chief whose Lebanese Forces party has one minister in the cabinet, said Syria was determined to stop the formation of the court.
Separately, John Bolton, the US ambassador to the UN, said that Lebanon's future is at stake in a battle between "democracy and terrorism" following the killing of Gemayel.
"The future of the Middle East, certainly the future of Lebanon, may well be decided in the next several days," Bolton told BBC radio on Saturday.
"A successful re-emergence of democracy there is being directly challenged by the terrorist Hezbollah and those who support them, Syria, Iran and others."
Bolton said it would be a "serious problem" if an investigation into Tuesday's assassination found Damascus was involved.
"Then you have a further clear piece of evidence that Syria is not just a supporter of terrorism but is a state actor in a terrorist fashion."