Ismail Ould Cheikh Ahmed said he was heading to Riyadh and Kuwait "to prepare for a new round" of talks, as he left Muscat late Saturday after discussions with representative of Yemen's Houthi Ansarullah movement, AFP reported.
The UN envoy said he found "a lot of seriousness" in talks with representatives of the Houthis from the party of former president Ali Abdullah Saleh.
He also said he had been in contact with US Secretary of State John Kerry who "sees a historic chance to achieve peace in Yemen".
A previous round of peace talks held in Kuwait collapsed in August.
A 48-hour ceasefire declared recently ended last Monday after Saudi warplanes repeatedly violated it.
On Saturday, 12 civilians lost their lives as Saudi warplanes struck two houses in the al-Marawi'ah district of Hudaydah province, located 150 kilometers southwest of the capital, Sana'a.
Separately, Saudi jets pounded a house in the al-Khawkhah district of the same Yemeni province, leaving a woman and a girl dead. Two people sustained injuries in the aerial attack.
Saudi Arabia has been engaged in a deadly campaign against Yemen since March 2015 in an attempt to bring back the former Yemeni government to power and undermine the Houthi Ansarullah movement.
The impoverished Arab country is grappling with the scarcity of food supplies and outbreak of diseases amid Saudi Arabia’s atrocious airstrikes.
The United Nations International Children's Fund (UNICEF) says 7.4 million Yemeni children are in dire need of medical help, and 370,000 run the risk of severe acute malnutrition.