ROME — The Houthi rebels who control the key Yemeni port of Hudaydah have agreed to enter talks about handing some control to the United Nations, its envoy to Yemen said during a visit to the city on Friday.

The initiative, although tentative, added to momentum for peace talks expected to start in the coming weeks, when the Saudi-led coalition and its Houthi foes are to meet in Sweden as a humanitarian crisis threatens to tip millions of Yemenis into starvation.

Hudaydah has been engulfed in fighting in recent weeks as the Saudi-led coalition has stepped up its assault there, partly surrounding it from three sides. That has prompted fears that the port, a major channel for food and fuel imports, could be cut off.

The United Nations sees a deal on Hudaydah as an important first step toward ending the war. But any arrangement to turn the port over to international supervision would also need approval from the United Arab Emirates, the Saudi ally leading the military assault.