Fneish was energy minister in the Western-backed government of Fouad Siniora, the Lebanese prime minister, before he and five other pro-Syrian ministers resigned last November.
Fneish said that Hezbollah was "in permanent contact" with another opposition stalwart, Nabih Berri, the parliamentary speaker.
"We support Mr Berri's initiative demanding that the majority respect the constitution on the necessity of a two-thirds quorum required to elect a new president," he said.
|Lahoud, the current president, is viewed by the|
governing camp as a pro-Syrian figure [AFP]
Berri has called a session of parliament for Tuesday to elect a successor to Emile Lahoud, Lebanon's current president and a pro-Syrian politican.
The president is elected by parliament, rather than by popular vote, and a two-thirds majority is required for a candidate to be elected.
In the event of a second round, a simple majority suffices.
Calls for increased security come after the killing of Antoine Ghanem, an anti-Syrian politician, and four other people by a car bomb in a Beirut suburb on Wednesday.
Lebanon's pro-government factions have blamed the attack on Syria, which denied involvement.
Ghanem was the eighth anti-Syrian politician to be assassinated since the February 2005 murder of Rafiq al-Hariri, a former prime minister.
Elias Attallah, head of the Democratic Leftist Movement, said on Sunday that "in order for the security to be total, the problem of the camp must be solved".
Attallah was referring to the tent city set up in the city centre near government offices and parliament by the Hezbollah-led opposition.
"The opposition must get rid of this encampment since it has renounced its claim of wanting a government of national unity and is now concentrating on efforts to find a consensus candidate for the presidency," he said.
Ghanem's assasination leaves the coalition government with 68 politicians in the 128-seat parliament.
It is not clear yet if the planned vote on Tuesday will take place.