But diplomatic pressure over the offensive, including from American officials, has injected new life into a possible cease-fire and peace deal, according to two diplomats familiar with the process. The two officials were not authorized to speak on the record to the media because of the sensitivity of the talks underway among United Nations officials, the Houthi leadership, the Emirati and Saudi governments and Mr. Hadi, who is supported financially by the Saudis.

Over the last week, Martin Griffiths, the United Nations special representative for Yemen, has been meeting with both Houthi leaders and Mr. Hadi, while other senior officials from the organization have been briefing Saudi and Emirati officials about a possible cease-fire, according to the two officials.

United Nations officials are also working to cement an agreement that would have the international body take over management of the Al Hudaydah port.

At the start of the battle for the city, Emirati officials said they had two key goals: controlling Al Hudaydah’s port and airport. The hope was the victory would be substantial enough to force the Houthis to sue for peace and give the Saudi- and Emirati-backed Yemeni factions a stronger role in future political negotiations.

While the Emirati-backed force has gained control of the airport, it has not launched its naval assault of the port, because of what Emirati officials say is heavy mining. American officials last month refused an Emirati request to help demine the waters around the city.

Another reason for the slowed offensive is that Emirati officials have said they do not want to engage in urban warfare, as they and their local proxies are not equipped to handle street-to-street combat.