The United Nations warned Thursday of an “incalculable human cost” in Yemen, potentially affecting hundreds of thousands of people, as an Arab force backed by the United States pressed toward the strategic Yemeni port city of Hodeida.

SANAA, Yemen —

“The situation has deteriorated dramatically in the past few days,” said Lise Grande, the top U.N. humanitarian official in Yemen. “Families are absolutely terrified by the bombardment, shelling and airstrikes. People are struggling to survive.”

A Saudi-led coalition seeking to restore Yemen’s internationally recognized government renewed its offensive near Hodeida within the past week after the failure last week of a U.N.-sponsored effort in Geneva to begin peace talks. The Yemeni rebels, known as Houthis, accused the coalition of preventing them from traveling with scores of their loyalists seeking medical treatment, while the coalition accused the rebels of purposely sabotaging the talks.

By the weekend, the coalition and allied Yemeni government troops resumed their advance on Hodeida, which is a critical gateway both for supplying the rebels and for transporting global assistance to address the world’s most severe humanitarian crisis. Nearly 70 percent of humanitarian aid and almost all commercial food stocks for northern Yemen flow through Hodeida.

A senior commander with the coalition and Yemeni government forces said Thursday that they had seized a key southern road to Hodeida, potentially weakening the rebels’ supply lines.

“We have taken control of the main southeast entrance and will move forward,” said Col. Adnan Almateri, the chief of joint operations in the area.

A senior Houthi political official disputed this, saying rebel forces still controlled the main southern entrance to Hodeida and had used roadside bombs and other means to stop their enemies.

“The coalition wants to take over the city and use that as a playing card to apply economic pressure on the Yemeni people and make them starve and therefore give in to the coalition,” said Dhaifallah Alshami, the Houthi official. “However, that will never happen. The will of the Yemeni people cannot be broken.

Inside Hodeida, residents reached by telephone said they were living in apprehension.

“We have been hearing heavy and midsize machine-gun firing, mortar shelling and airstrikes in the outskirts of the city, near the entrance of the city, especially at night for the past few days,” said Mazen Mujammal, 21. “There is a great sense of panic and fear among people.”

He and other residents said that the city was suffering shortages of food and medicine and that the rebels were patrolling the streets. Most shops and restaurants have closed. It was difficult for most residents to flee because of the ongoing clashes near the entrance to the city.

“The shootings and bombings are outside the city, in the southern part,” said Majed Qadoo, 35, a government employee. “Inside the city, the situation is stable. People fear, however, that the bombings and shootings will reach them inside the city.”

Almateri, the coalition commander, vowed that coalition troops would march into Hodeida.

“There will be no dialogue with the enemy or stopping before liberating the country from them. They do not seek peace and are nothing but a destruction tool,” Almateri said. “The coming days will carry more and more surprises and, with God’s will, we will defeat this criminal gang.”

The renewed push by the coalition comes as the Trump administration on Wednesday said it stood behind the coalition, which includes forces from Saudi Arabia and the United Arab Emirates, despite mounting international criticism that their airstrikes have killed and injured thousands of Yemeni civilians. That certification, in which the administration told Congress that the coalition was taking measures to prevent such casualties, allows the United States to keep refueling coalition warplanes as well as supplying the coalition with intelligence and weaponry.

After more than three years of civil war, some 22 million people, nearly 75 percent of Yemen’s population, need humanitarian assistance, with 8 million on the brink of starvation, according to the United Nations. Thousands have died of preventable diseases.

If Hodeida becomes engulfed by conflict, the humanitarian crisis is likely to worsen. U.N. staffers are particularly worried about the grain mills there, which help feed millions of people, Grande said.

“If the mills are damaged or disrupted, the human cost will be incalculable,” Grande said. “So much has already been destroyed. In the last six weeks alone, houses, farms, livestock, businesses, roads, a water facility and a flour mill have all been hit.”

Raghavan reported from Cairo.