"We hope that his (Griffiths's) visit to Riyadh ends with positive results," Huthi told reporters after their talks.
"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 on what was his first visit to Hodeida.
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.
According to UN figures, nearly 10,000 people have been killed since the coalition joined the conflict in 2015 to bolster Hadi, triggering what the UN calls the world's worst humanitarian crisis.
Rights groups fear the actual toll is far higher.
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