"I'm greatly reassured by the messages I have received, which have been positive and constructive," Martin Griffiths told reporters at Sanaa airport after two days of talks in the rebel-held capital.
"I'm especially thankful to Abdul Malik al-Huthi, whom I met yesterday, for his support and the fruitful discussion we held."
Griffiths said he would brief the UN Security Council on Thursday on his latest talks in Yemen, where a brutal war between the rebels and the Gulf Arab-backed government threatens to engulf Hodeida, the entry point for desperately needed humanitarian aid.
In the coming days, the UN envoy is to meet President Abedrabbo Mansour Hadi, whose loyalists have reached the southern outskirts of the Red Sea port city with support from Emirati troops.
UN envoy visits Yemen for talks on key port city
"All parties have not only underscored their strong desire for peace but have also engaged with me on concrete ideas for achieving peace," Griffiths said.
Hodeida is the latest battleground in the Yemeni conflict, which has killed nearly 10,000 people since 2015, 2,200 of them children, and pushed the country to the brink of famine.
The Red Sea port provides a lifeline for the 22 million Yemenis dependent on humanitarian aid and is also the point of entry for three-quarters of the country's commercial imports.
The government and its allies in a regional coalition, led by Saudi Arabia and the United Arab Emirates, accuse the Iran-backed rebels of receiving smuggled weapons through Hodeida and have demanded their unconditional withdrawal from the city, which they have held since 2014.
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