"We demand the prime minister announce openly and clearly his commitment (to the tribunal) before parliament on Tuesday and say that he will take all necessary steps to abide by its decisions, or get out, he and his government," said a statement read by MP Fuad Siniora, himself a former premier and leading member of the pro-Western opposition.
Three days of parliamentary talks begin on Tuesday, ending with a vote of confidence on Mikati's government in which Hezbollah and its allies control the majority of seats, including the key telecommunications and justice ministries.
The alliance led by the Iranian- and Syrian-backed group also holds a slight majority in parliament.
The vote comes days after the UN-backed Special Tribunal for Lebanon issued an indictment in the 2005 assassination of Hariri, a powerful Saudi-backed Sunni billionaire and politician, implicating four Hezbollah operatives in the murder.
In a statement released by his office Monday, Mikati accused the opposition of launching a "violent campaign" against the government, which the opposition has refused to join on grounds it is controlled by Hezbollah.
The premier defended his government's program, saying it stipulated "respect" for international resolutions, including the 2007 UN Security Council resolution upon which the tribunal was founded.
Mikati's government program includes an ambiguously worded clause stipulating that Lebanon will respect international resolutions as long as they do not threaten peace and stability.
But the opposition led by former premier Saad Hariri -- son of Rafiq -- has demanded Mikati state his government is "committed" to the tribunal.
The Special Tribunal for Lebanon has triggered a deep political crisis in Lebanon, leading to the collapse in January of Saad Hariri's Western-backed unity government.
Hassan Nasrallah, leader of Iranian-backed Hezbollah, on Saturday said he would never hand over the four, adding the Netherlands-based court was heading for a trial in absentia.
Nasrallah has repeatedly dismissed the tribunal as a US-Israeli conspiracy against his armed party but on Saturday struck a conciliatory tone, saying Israel's attempts to incite sectarian violence in Lebanon would fail.
Among those indicted by the tribunal for the February 14, 2005 bombing that killed Hariri and 22 others in Beirut is Mustafa Badreddine, brother-in-law of Hezbollah commander Imad Mughniyeh, assassinated three years ago in Damascus.
The indictment comes at a delicate time for Hezbollah, as its ally Syrian President Bashar al-Assad faces an unprecedented domestic uprising against his rule.
The Hariri murder sparked a wave of massive protests in Lebanon in 2005 which, combined with international pressure, forced Syria to withdraw its troops from the country, ending a 29-year deployment.
Syria was widely suspected of having a hand in Hariri's murder but has denied any involvement.
BEIRUT (AFP) -- Lebanon's opposition has demanded Prime Minister Najib Mikati announce his full support for a UN-backed court charging Hezbollah members in ex-premier Rafiq Hariri's murder, ahead of a vote of confidence.