At stake is a ceasefire in Yemen, where four weeks of Saudi Arabia's military campaign have caused hundreds of civilian casualties and added a new layer of hardship to an existing humanitarian crisis by imposing a naval blockade.
President Abd-Rabbu Mansour Hadi and his government in exile in Riyadh say they will only talk if the Houthis quit cities they have occupied, particularly the port of Aden, and lay down their arms.
For their part, the Houthis say they will talk only if the air strikes stop completely.
To date, those talks have yet to start, according to Yemeni Foreign Minister Reyad Yassin Abdulla, who said there was no communication between the government and the Houthis.
"There can be no communication until they put their weapons aside," he told reporters on a visit to Bahrain, adding talks could start only when the Houthis also withdrew from all cities and the situation stabilized.
Hadi's position is backed by Saudi Arabia, which despite announcing an end to its bombing campaign on Tuesday, is still using air strikes to target military activity by the Houthis and their allies in Yemeni cities.
A purported Omani proposal circulated by Yemeni government officials this week was drafted along those lines, also stipulating that Hadi and his government be allowed to resume their position.
In return, according to the proposal, all parties would prepare for presidential and parliamentary elections soon, and Yemen's economic and humanitarian crisis would be addressed with international aid and investment.