Mohammed Fneish, a Hezbollah member who resigned as a minister in November, said the decision was "a positive step as it signals a will to reach an agreement and pursue efforts to reach a consensus."
Electing a president suitable to the ruling March 14 coalition and the Hezbollah-led opposition is seen as intrinsic to resolving a political deadlock between the two factions.
The ruling coalition has put forward two names for the presidency, which is reserved for a Maronite Christian.
The opposition is insisting on another candidate from outside the March 14 camp.
Analysts predict that both sides will only reach an agreement on a consensus candidate in the final 10 days of Lahoud's mandate, when parliament will be in permanent session.
There are concerns that Lebanon could end up with two rival governments if no agreement is reached on a consensus presidential candidate by the time Lahoud's term runs out on November 23.
Opposition MPs boycotted parliament on September 25 to prevent a necessary two-thirds quorum from forming for the election of a new head of state.
Fouad Siniora, Lebanon's prime minister, is supported by the United States and Saudi Arabia, who want to replace Lahoud with a president more amenable to their influence.
Hezbollah, which has ties to former occupier Syria, wants to prevent the presidency from being taken by a pro-US candidate.
Many Lebanese fear that another MP from the ruling coalition could be assassinated, following the murder of Antoine Ghanem, a March 14 MP, and five others in a car bomb attack days before the previous parliamentary session.
Ghanem was the sixth Lebanese politician to be killed since 2005 in attacks blamed by the ruling coalition on Syria, which has denied involvement.