The talks come amid signs that an agreement remains elusive on the two issues that threaten to destabilise the country.
The discussions, which began on 2 March, have focused on a 2004 UN Security Council resolution that calls for disarming Hizb Allah and Palestinian fighters.
The resolution also urged new presidential elections.
It was passed in September 2004, days before Lebanese legislators extended Emile Lahoud's term for three years.
Wednesday's talks came ahead of a visit later this week by Terje Roed-Larsen, the UN Middle East envoy, who was expected to push for the implementation of UN Resolution 1559.
Reflecting a pessimistic view of the outcome of the conference, the leading An-Nahar daily said in its banner headline on Wednesday: "The resumption of the national conference: No solutions and no crisis."
In a similar vein, another Beirut daily, As-Safir, predicted that Wednesday's round would be postponed until after the forthcoming Arab summit because the leaders have failed to reach an "acceptable formula" for the presidency issue and the future of Hizb Allah's weapons.
Berri: No decisions on Lahoud or
Hizb Allah are expected soon
The paper quoted Nabih Berri, the Parliament speaker, as saying that no decisions on Lahoud or Hizb Allah were expected from Wednesday's meeting.
Anti-Syrian groups are pushing for Lahoud to step down, accusing him of being too close to Syria.
Although the groups have a majority in parliament, they do not control the two-thirds majority needed to force the president to resign.
They also have accused Damascus of being behind last year's assassination of Rafiq al-Hariri, the former prime minister.
Syria denies involvement in the assassination.
Part of the anti-Syrian camp wants Hizb Allah to disarm.
Lahoud has vowed to stay in office until the end of his term next year, but, in an interview with Aljazeera on Saturday, he proposed early parliamentary elections as a way out of the stalemate.
He also rejected calls for Hizb Allah to disarm, saying it should keep its weapons until a comprehensive Arab-Israeli settlement is reached.