The UN's current peace push in Yemen is the biggest since 2016 when 108 days of negotiations in Kuwait failed to yield a deal between the government and Iran-aligned Houthi rebels.
UN envoy Martin Griffiths met a Yemeni rebel leader in rebel-held Sanaa on Saturday and is to follow up by holding talks with Yemen's government in Riyadh, a UN source said.
In a possible breakthrough despite scepticism on the government side, the envoy has said he has opened a dialogue with Houthi rebel officials on "how the UN could contribute to keeping the peace" in the key port city of Hudaida.
The UN source said Griffiths will hold talks on Monday in the Saudi capital, where Yemeni President Abedrabbo Mansour Hadi and other officials have taken up residence.
On Saturday, Mohammed Ali al Houthi, head of the Houthi rebels' Higher Revolutionary Committee, met in Sanaa with the UN envoy, an AFP photographer said.
"We hope that his (Griffiths's) visit to Riyadh ends with positive results," Houthi told reporters after their talks.
Griffiths arrived on Wednesday in Yemen ahead of planned peace talks in Sweden in December between the Iran-aligned Shia Houthi rebels and pro-government forces backed by a Saudi-led military coalition.
No date has yet been set for the negotiations.
The UN-recognised government had not yet received "any information from UN envoy Martin Griffiths about the talks in Sweden and what is to be discussed", Rajeh Badi, a government spokesman, said on Friday.
"We are certain that the Houthi rebels have not yet taken a strategic and serious decision about peace," he told AFP.
"They (Houthis) will not let go of their weapons. They would tell us: 'You're dreaming if you think we're going to disarm.'"
Griffiths, however, struck a positive note on Friday during his first to Hudaida.
"I am here to tell you today that we have agreed that the UN should now pursue actively and urgently detailed negotiations for a leading UN role in the port," he told reporters.
Griffiths urged Yemen's warring parties to "keep the peace" in the rebel-held Red Sea port city, which serves as the entry point of nearly all imports and humanitarian aid into the impoverished country.
UN agencies say 14 million Yemenis are at risk of starvation and the closure of Hudaida port would further exacerbate the humanitarian crisis.
Biggest peace push since 2016
Under heavy international pressure, the loyalists and their Saudi-led military backers have largely suspended a five-month offensive on Hudaida.
Humanitarian organisations are desperate to see the current peace push translate into a more permanent halt to Yemen's four-year war.
The current peace push is the biggest since 2016.
In September, UN-led peace talks faltered when the Houthis refused to travel to Geneva, accusing the world body of failing to guarantee their delegation's return to Sanaa or secure the evacuation of wounded rebels to Oman.
Previous talks broke down in 2016, when 108 days of negotiations in Kuwait failed to yield a deal and left rebel delegates stranded in Oman for three months.
The conflict in Yemen, which escalated when the Saudi-led alliance intervened in 2015, has killed nearly 10,000 people and left up to 22 million Yemenis in need of humanitarian assistance, according to UN figures.
Rights groups fear the actual death toll is far higher.
The Arab coalition joined the conflict a year after Houthi rebels captured Sanaa to bolster Hadi, triggering what the UN calls the world's worst humanitarian crisis.