The source said the decision to hold demonstrations had been agreed between Hassan Nasrallah, the Hezbollah leader; Nabih Berri, the parliament speaker; and Michel Aoun, the Christian opposition leader.
"Fouad Siniora, the Lebanese prime minister, has said his cabinet is constitutional ... and has vowed not to step down"
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The resignation of the six pro-Syrian ministers after the anti-Syrian majority coalition rejected their demands for a decisive say in government led the opposition and Emile Lahoud, Lebanon's pro-Syrian president, to say the government was no longer legitimate.
They say its decisions, including its agreement to try suspects in the assassination of Rafik al-Hariri, the former prime minister, in an international tribunal, are unconstitutional.
Fouad Siniora, the Lebanese prime minister, has said his cabinet is constitutional.
He has vowed not to step down and called on the ministers who have resigned to rejoin the government.
Anti-Syrian elements in Lebanon say Hezbollah and its allies want to weaken Siniora's government and derail its plans for the international tribunal.
A UN inquiry has implicated Syrian and Lebanese security officials in the 2005 killing of al-Hariri. Syria has denied involvement.
Hezbollah has also criticised Siniora's cabinet for what it says was the government's failure to back it during its July-August war with Israel.
Critics are concerned that any widescale protests could disintegrate into street-level violence, deepening the political crisis and escalating sectarian tensions.
Since the assassination of Pierre Gemayel, the anti-Syrian cabinet minister, on November 21, hundreds of soldiers and police have been deployed on the streets of Beirut.
General Michel Suleiman, a commander in the Lebanese army, told soldiers to "keep the same distance from everybody and to preserve the security of all citizens, including the opposition and loyalists".