They called on the pro-Syrian president "to resign immediately and will give him until March 14", in a statement issued on Thursday after the leaders of the majority group held a meeting in Beirut.
They called on MPs of the parliamentary majority to sign a petition calling for the ousting of Lahoud, but did not specify what measures they would take if Lahoud refused to budge.
Participants in the previously unannounced meeting included Saad al-Hariri, the son of the slain former prime minister Rafiq al-Hariri; Druze leader Walid Jumblatt; the leader of the Christian Lebanese Forces group, Samir Geagea; and other politicians.
A statement read to reporters by former lawmaker Fares Soeid said: "The participants have decided to go ahead with a political and popular campaign by asking lawmakers ... to immediately sign a parliamentary petition requesting an end to Emile Lahoud's term."
The deadline of 14 March referred to the date of a massive rally 11 months ago held to commemorate the killing of al-Hariri. Almost one million people, or one in four of Lebanon's population, took part.
The president's term in office was extended by three years to the end of November 2007 under a controversial Syrian-promoted constitutional amendment adopted in September 2004.
On Wednesday, Lahoud vowed to complete his mandate despite growing pressure to stand down after another massive rally for al-Hariri, in whose 14 February 2005 murder the Syrian intelligence services have been implicated.
He "has not and will not give up on his belief in a united Lebanon and will stay on until the last day of his mandate", Lahoud's office said.
The Lebanese president slammed the "incitement" of the anti-Syrian camp that he said was damaging to Beirut's ties with other Arab states. Their attacks were aimed at "masking rifts" within their own ranks, he said.
Almost 1m people took part in
the 14 February Beirut rally
The anti-Syrian group has 70 MPs in parliament, but it would need two-thirds of votes in the 128-seat house, or 85 seats, to force the president's resignation.
Also on Thursday, Hasan Nasr Allah, secretary-general of the Syrian- and Iranian-backed Shia Lebanese organisation Hizb Allah, urged Lebanese factions to adopt dialogue to solve their differences.
Hizb Allah surprised observers when it did not join the demonstrations held in Beirut on the first anniversary of al-Hariri's assassination. Lebanese political leaders seized the opportunity to deliver harsh anti-Syrian speeches.
"Any party adopts any mean other than dialogue will lose," he said.
He lashed out at the anti-Syrian alliance and warned that some groups are pushing towards civil war by focusing on sectarian and short-term tactical goals.
Towards civil war
"Most of the speeches delivered on 14 February will push Lebanon towards a civil war, so the government has to clarify its position," Nasr Allah said.
"We work for the interest of Lebanon. We are not involved in any alliance.
Nasr Allah lashed out at the
anti-Syrian alliance's message
"If we are to join any alliance, we will choose an anti-Israel and America alliance," Nasr Allah said.
Hizb Allah is facing growing demands to give up its arms and integrate its fighters with official Lebanese forces.
"From the very beginning, Hizb Allah's arms have been national Lebanese and not the Shias'. The former Lebanese prime minister himself [al-Hariri] linked the issue of the resistance arms to reaching a settlement with Israel," Nasr Allah said.
The Hizb Allah chief thanked Syria and Iran for backing what he called resistance against Israel.
"The resistance which protected Lebanon will remain revered, and the weapons that liberated the [occupied] land will remain sacred too," he said.