AL HUDAYDAH, Yemen — The battle for Al Hudaydah, the Yemeni port city and lifeline to a nation threatened with famine, intensified on Tuesday as warplanes from a Saudi-led, Western-backed Arab coalition pounded targets citywide in an effort to drive out Iran-allied Houthi rebels.

Fighters exchanged fire over mine-infested ground at the disused international airport south of the city. Houthi tanks fired shells to defend a key coastal road. Rebels dug trenches into approach roads, in anticipation of a fight for the city center.

Even with all that, the port kept operating.

Dock workers hastily unloaded three ships sent by the United Nations World Food Program that contained enough food for six million people for one month, a spokeswoman, Bettina Luescher, told reporters in Geneva. The sheer amount was a reminder of how the fate of Al Hudaydah has become tied to the fate of millions of vulnerable Yemenis.

The stream of trucks that trundles from the Red Sea port account for about 70 percent of imports in a country where two-thirds of the 29 million people rely on international aid. Aid groups warn that any interruption to that movement would cut supplies to eight million people on the edge of starvation, and cause a sharp rise in food prices for other Yemenis, potentially tipping them into danger.