Qatari Prime Minister Sheikh Hamad bin Jassem bin Jabr al-Thani "offered to come up with a proposal on the Hezbollah weaponry issue and present it to the two parties," a Lebanese delegate told reporters.
"The two sides have agreed to that," he added following the first session of Arab-mediated talks by 14 leaders or representatives of the government and the Hezbollah-led opposition, backed by Syria and Iran.
Host Qatar offered to come up with a compromise after leaders of the March 14 parliamentary bloc insisted on listing Hezbollah's arms on the agenda of the dialogue, said the delegate, requesting anonymity.
After 65 people were killed in nearly a week of fighting, the two sides agreed on Thursday to a national dialogue aimed at breaking an impasse over electing a new president and forming a unity government.
The Qatari hosts will be working against the backdrop of two United Nations Security Council resolutions calling for the disarmament of all militias in Lebanon.
Hezbollah was the only group that did not have to hand over its guns to the government following the 1989 Saudi-brokered Taef agreement to end the 1975-1990 civil war, because it was fighting the Israeli occupation of south Lebanon.
However, Israel pulled its troops out of Lebanon in 2000.
Resolution 1559, adopted in 2004 called, among other things, for the "disbanding and disarmament of all Lebanese and non-Lebanese militias."
Resolution 1701, which brought an end to the 2006 war between Israel and Hezbollah, called for there to be "no weapons or authority in Lebanon other than that of the Lebanese state."
Despite disagreement over the arms question, the delegates did agree to form a committee of three members from each side to address the issue of a new electoral law for parliamentary polls due next year, the delegate said.
No time has been fixed for the next session, said a source in the Arab League, which is sponsoring the crisis talks, but bilateral meetings were expected to be held on the sidelines of the gathering.
In addition to the electoral law, the leaders are expected to discuss a proposed unity government.
Parliament has failed to convene to elect a successor, exacerbating a crisis that began in late 2006 when six pro-Syrian ministers quit the cabinet of Prime Minister Fouad Siniora.
On June 10, it is due for the 20th time to meet to elect a president.
The talks officially started on Friday evening with a brief opening session chaired by Qatar's emir, Sheikh Hamad bin Khalifa al-Thani.
Mediation continued overnight with the emir shuttling between rival parties, according to the Lebanese pro-government newspaper An-Nahar.
Hezbollah leader Hassan Nasrallah is not attending, reportedly because of security concerns, and is represented by Hezbollah MP Mohammed Raad.
Also attending on behalf of the opposition are parliament speaker Nabih Berri and Christian leader Michel Aoun.
The dialogue is linked to a six-point plan agreed following Arab League mediation led by the Qatari premier.
Under the deal the rivals undertook "to shore up the authority of the Lebanese state throughout the country," to refrain from using weapons to further political aims and to remove militants from the streets.