The court is at the heart of Lebanon's worst political crisis since the 1975-1991 civil war.
The coalition backing Siniora accuses the opposition of trying to thwart the tribunal's establishment to protect its allies in the Syrian government.
Majority leaders accuse Syria of the 2005 assassination of al-Hariri and a string of other attacks on government figures. Syria denies involvement in any of the attacks.
The attacks are being investigated by a UN investigation.
The government has been demanding a session of parliament so that ministers can vote on the tribunal draft.
But Nabih Berri, parliament speaker and opposition leader, says he will not call it to debate the tribunal until there is a new government.
The opposition, which includes Hezbollah, disputes the legitimacy of the government which approved the tribunal statutes in November.
The opposition says it agrees with the idea of the tribunal but wants to discuss its mandate so it is not used as a political tool.
Ban said during a visit to Lebanon late last month he wanted the issue to move forward but that it was premature to talk about setting up the tribunal under Chapter 7 of the UN charter when Lebanese constitutional procedures had yet to be taken towards approving the court.
Chapter 7 makes Security Council resolutions mandatory under international law.