The talks, which resumed after a five-day break on Monday, are intended to end the country's political paralysis, which set in after Syria pulled out its troops after maintaining a military presence in its tiny neighbour for 29 years.
Nabih Berri, the parliamentary speaker, told journalists after the meeting that lasted fewer than three hours that the "Talks focused on one essential subject, that of the presidency of the republic ... and this point remains on the agenda for the next session, next Monday".
Officials said that the question of the presidency could only be resolved once the subject had been discussed on the fringes of the two-day Arab summit in Khartoum, which starts on Tuesday, possibly with Bashar al-Assad, the president of Syria.
Fawzi Sallukh, the foreign minister of Lebanon, said in the Sudanese capital that "the question may be discussed during discussions on the margins of the summit between the Syrian and Lebanese presidents".
"Talks focused on one essential subject, that of the presidency of the republic ... and this point remains on the agenda for the next session, next Monday"
Bassem al-Sabeh, an MP with the anti-Syrian majority in parliament, told the al-Mostaqbal daily: "The Arabs must intervene in the departure of Lahoud," as his presidential mandate was extended by an Arab country - Syria.
Evidence of the gulf between the two sides over Lahoud showed clearly in the decision of Fuad Siniora, Lebanon's prime minister, to attend the summit in addition to Lahoud, believing this would better represent the country.
"This decision (for Siniora to go) is aimed at making up for the inadequate representation of Lebanon which is limited to the president of the republic," said a government source, who asked not to be named.
The anti-Syrian majority in Lebanon's parliament has contested Lahoud's right to represent the country at the summit, arguing that he is only still in office as his mandate was extended by Syria.
The source pointed out that MPs from the anti-Syria parliamentary majority had protested at Lahoud's attending the summit.
In a letter to Arab leaders, they said Lahoud's participation was an "attack on the constitutional legitimacy" of the country because his position as head of state "resulted from the extension of his presidential mandate by Syria".
But presidential sources quoted by the press said the renewal of Lahoud's mandate was constitutional and recognised by the Arab countries.
"The Arabs must intervene in the departure of Lahoud"
A diplomatic source said that Saniora was initially reticent about going to a summit attended by Lahoud but was persuaded after meeting Saudi King Abdullah on Sunday.
The source said the king had indicated that Syria was ready to show itself cooperative.
Given the power struggle in Beirut, both Lahoud and Siniora travelled separately on Monday to Khartoum.