Pro-Syrian Lebanese President Emile Lahoud has said the government has lost its legitimacy after a series of ministerial resignations.
Lahoud: "What is based on illegal grounds shall be considered null and void"
He said any cabinet meeting now would be worthless and anti-constitutional.
Ministers from Hezbollah and the other pro-Syrian Shia Muslim group, Amal, resigned on Saturday.
The government is due to discuss a draft UN document on a tribunal for those suspected of killing anti-Syrian former PM Rafik Hariri last year.
Tension in Lebanon has been building since this summer's conflict between Hezbollah and Israel, and ahead of the formation of the tribunal.
Prime Minister Fouad Siniora, who is part of the anti-Syrian parliamentary majority, has refused to accept the ministers' resignations.
Hezbollah, which had been demanding a more powerful role in the government, has said it will not retract them.
It has threatened to hold mass protests unless its demands for more cabinet seats are met.
In multi-party talks, Hezbollah had asked for cabinet seats that would give it and its allies the power of veto but the majority group in parliament refused.
Health Minister Mohammed Jawad Khalifa, one of those who resigned, told the BBC the current cabinet did not reflect recent changes in the Lebanese political landscape.
"What happens when we reach a dead end?" said Mr Khalifa.
"Someone has to take responsibility. Our resignation is a result of not resuming the dialogue. There are no more consultations, and there are differences - so things have come to an end."
The BBC's Kim Ghattas in Beirut says the resignations were something of a surprise as there had been hope that the power-sharing talks would resume at a later date.
Hezbollah asked for power of veto at the multi-party talks
The ministers who resigned were in charge of the foreign affairs, agriculture, health, energy and labour portfolios.
More than eight ministers would need to resign for the government to fall.
Mr Lahoud opposed the cabinet meeting, saying he needed more time to study the draft.
On Sunday, he deepened his opposition, saying: "Any cabinet meeting held by this government shall be absolutely illegal and unconstitutional because what is based on illegal grounds shall be considered null and void."
Our correspondent says the move could make things very difficult for Western-backed Mr Siniora.
She says Mr Siniora could appoint five different Shia ministers, but politically this would add to the growing tension in Lebanon between pro-Syrian groups and the anti-Syrian coalition government.
Hezbollah has accused the Lebanese government of failing in its job, and has proclaimed itself the victor of the conflict with Israel earlier this year.