Lebanon's President Emile Lahoud says he opposes his government's approval of UN plans to try suspects in the killing of former PM Rafik Hariri.
Mr Lahoud says the current cabinet is unconstitutional
Mr Lahoud said Monday's cabinet decision was not constitutional because as president he had not endorsed it.
Hezbollah also rejected the move because all five Shia ministers had resigned before the cabinet vote.
The UN has implicated Syrian officials in the bombing that killed Mr Hariri in 2005, but Damascus denies involvement.
"The cabinet's approval of the plans... are not binding on the Lebanese state," Mr Lahoud said in a letter to UN Secretary General Kofi Annan.
He said the resignation of the five Shia ministers on Saturday, plus a Christian minister on Monday, meant that the cabinet no longer represented all religious groups as required by the constitution.
Hezbollah's leader, Sheikh Hassan Nasrallah, promised to replace the cabinet with "a clean-handed government".
"This government will go, and we have nothing to do with it after the resignations. A new government will come," the As-Safir newspaper quoted him as saying.
Hezbollah, which regards its month-long conflict with Israel earlier this year as a victory, is seeking a one-third-plus-one share of cabinet seats for itself and its allies, giving them effective veto power.
The latest draft of the UN tribunal plan has not been made public, but it is thought that the tribunal will sit outside Lebanon, possibly in Cyprus.
The tribunal's statutes will rely on a mixture of Lebanese and international law, and Lebanese and international judges will sit on the tribunal.
It is believed that the death sentence will not apply in the case of guilty verdicts.