Nabih Berri, the parliamentary speaker, and an ally of the Hezbollah-led opposition said he will not acknowledge the poll results.
Mohammed al-Amin Itani of the ruling majority is expected to replace Eido's seat since the opposition did not officially sponsor a candidate.
|Amin Gemayel will run for his late son's seat on behalf of the ruling party [AP]|
However, the vote in the Christian stronghold of Metn for Gemayel's seat is expected to be fiercely contested.
Amin Gemayel, Lebanon's president for much of the 1980s, has decided to compete for his son's seat on behalf of the ruling party.
He faces off against Kamil Khoury, who is supported by Michel Aoun, a former army commander and prime minister allied with the opposition.
His party dominated in legislative district elections in 2005.
Tensions have been high in Metn, and several clashes have been reported between Aoun and Gemayel's supporters over the past week.
"The army command, internal security forces and all security agencies will not allow any trouble, and the measures will be strict," Hassan Sabei, the interior minister, said.
"This is a free democratic process," he said on Saturday after deploying his forces in the two election districts.
Antoine Suleiman, the Mount Lebanon governor, ordered that all nightclubs, bars and cafes and other places selling alcohol in the Metn region be closed over the weekend.
Suleiman also banned the use of fireworks starting Monday at noon when the results are expected to be released.
Cardinal Nasrallah Sfeir, leader of the Maronite Christian church, has attempted to mediate between the Christian factions to avoid tension elections.
Gemayel and his allies have accused Damascus of masterminding the assassination of his son Pierre and a number of other anti-Syrian politicians in the past two years.
They believe that Syria has an agenda to end the majority's rule through a campaign of attrition.
Syria however has denied the allegations. "Metn will not become part of Damascus' countryside. Metn will not become a new field to erect tents for sit-ins," Gemayel said during a rally on Friday, referring to an opposition sit-in that began on December 1 in outside Siniora's office.
The standoff between Siniora and the opposition threatens to tear the country apart and could lead to the formation of rival government factions if parliament fails to elect a new president before the deadline for Lahoud to step down on November 23.