"I call on all parties to renew their commitment to this truce for five more days at least," UN envoy to Yemen Ismail Ould Sheikh Ahmed said at the summit's opening in the Saudi Arabian capital, Riyadh.
"This humanitarian truce should turn into a permanent ceasefire," he added.
Approximately 400 Yemeni tribal leaders and politicians, including leading figures of former Yemini President Ali Abdullah Saleh's party the General People's Congress (GPC), are attending the three-day summit to hash out a solution for the conflict.
Abdulaziz al-Jaber, head of the summit's organizing committee, said that the goals of the talks are to prepare a constitution to be presented to Yemen's people and "to hold a referendum to put the results of the dialogue into practice."
"We reassure the people that restoring the state is inevitable," al-Jaber added.
However, the Houthis and a majority of Saleh's supporters have boycotted the three-day meeting, which began on Sunday.
Khaled Bahah, the vice president of Yemen's internationally recognized government, said on Sunday his administration is in favor of the ceasefire extension.
"We need the ceasefire to continue for long, not just for a few days, but it depends on the operation on the ground," Bahah told Reuters in Riyadh.
"There is an effort for an extension, but it depends on how it is on the ground," he added. "But it's our wish from the government side that we need to extend it."
While the five-day ceasefire allowed humanitarian assistance to enter the country, aid organizations have said it was not long enough. The fragile truce is scheduled to expire Sunday evening.
Meanwhile, 15 were killed in clashes on Saturday night as militias loyal to President Abed Mansour Hadi continue to engage with Houthi rebels in the city of Taiz and Dhalea.
The UN has condemned the conflict, citing the high number of civilian casualties. More than 1,400 people have died since the Saudi-led operation began airstrikes in March, according to UN figures.
ls/sms (AFP, AP, Reuters)