HUDAYDAH, Yemen — The fight in Yemen has escalated drastically over the past week, exacerbating a dire humanitarian crisis that the United Nations says could spiral into famine — despite, or even because of, a diplomatic push by the United States to get both sides to the peace table.

The Saudi-led coalition, which the United States has armed and supported, has launched a punishing wave of airstrikes against the rebel Houthis. The warplanes have hit targets in the capital, Sana; in the mountainous northern provinces; and in the Red Sea port of Hudaydah where, aid workers warn, the country’s main humanitarian lifeline hangs by a thread.

A senior aid worker and two Western officials, who asked not to be identified so they could speak openly about Hudaydah, said in interviews that the coalition, commanded locally by the United Arab Emirates, had redoubled its five-month offensive to snatch the city from Houthi control.

Columns of Yemeni militias fighting under the coalition flag have burst across a major front line and swept through the desert on the eastern edge of the city, threatening to encircle it completely, they say. Warplanes and attack helicopters have pummeled Houthi positions in the city in what aid workers called a near-continuous barrage of air attacks.