The port’s cranes rise above a nearby shantytown in Hodeida, Yemen, the center of a civil-war offensive. (Abduljabbar Zeyad/Reuters)

Thousands of civilians continue to flee the strategic port city of Hodeida while those remaining are gripped by perpetual fear of airstrikes, said residents and aid workers this week as diplomats press for a cease-fire and peace talks.

The offensive for Hodeida, launched last month, is widely seen as a critical juncture in Yemen’s three-year civil war pitting northern rebels against the Yemeni government, which is backed by a regional coalition led by Saudi Arabia and the United Arab Emirates.

The city’s port is a vital gateway for food, medicine and other crucial supplies to rebel-held areas in a country gripped by the world’s worst humanitarian crisis. A prolonged battle for the city of 600,000 residents could lead to the deaths and displacement of hundreds of thousands of people, the United Nations has warned.

More than 121,000 residents have fled the city and other parts of the province since June 1, the U.N. said this week.

Those who remain in the city are in limbo, unsure when the fighting will reach their neighborhoods. The streets are mostly empty, as residents hunker down inside their homes. Most shops and businesses are shuttered, residents said.

People displaced by the fighting near Hodeida line up for U.N. aid on June 27. (Abduljabbar Zeyad/Reuters)

“We don’t know what the coming days will bring, but we pray that Allah will keep us safe,” said Mohammed Noori, 28, a resident in the eastern part of the city, all of which is under the control of the rebels, known as the Houthis.

The collective fears persist even as the UAE, whose forces and allies are leading the offensive for Hodeida, announced a pause in its assault on the city to allow time for U.N. envoy Martin Griffiths to broker a peaceful resolution. On Wednesday, Griffiths met with the Houthis’ leaders — talks he described as productive — and he briefed the U.N. Security Council on Thursday before meeting in the coming days with the exiled Yemeni government.

Diplomats are also counting on the backing of Iran, which supports the Houthis, in sealing an agreement that will eventually allow the U.N. to control Hodeida’s port.

Iran has been “very cooperative” in recent months on Yemen, said a senior international diplomat involved in efforts to end the war who spoke on the condition of anonymity to discuss the sensitive negotiations freely. Struggling against newly reimposed U.S. sanctions, Tehran is “under pressure to show something nice for the international community.” In general, the diplomat said Yemen was a “sideshow” for Iran and basically just a way to irritate the Saudis, who largely entered the war fearing that Iran is seeking to gain regional influence through the Houthis.

“I think Iran is ready for an agreement” on Yemen, the diplomat said.

Previously, he added, there had been a deal with both sides to allow the U.N. to control the Hodeida port, but it fell apart because the Houthis insisted that they keep control of the city of Hodeida. A senior Houthi leader on Thursday blamed the coalition for the lack of an agreement, saying that coalition forces have continued their push to take the city.

“We don’t mind stopping the fighting in Hodeida in order to enter comprehensive and complete negotiations,” said Saleem Mughalles, a member of the rebels’ political bureau. “However, the coalition should stop the fighting there. The fighting is still ongoing until this moment.”

On Thursday, aid agencies working in Yemen urged all sides to broker a deal.

“U.S., British, French and Iranian diplomats must do all they can to push the warring parties to cooperate with the U.N. envoy in agreeing on an immediate cease-fire and a new round of peace talks,” Mohamed Abdi, country director for the Norwegian Refugee Council, said in a statement via email. “We cannot allow a continued battle for [Hodeida] to take more innocent lives of a people who have already been through an unbearable amount of suffering.”

On the ground, the fighting intensified this week in and around the city, although the situation on the ground remained largely static, the aid group said, adding that the city “remains largely calm, but tense.” Fuel, gas, food and water are available, but there are widespread blackouts, residents said. Some described Hodeida as a “ghost city.”

“There is no movement on the streets,” said Noori, the Hodeida resident. “Most families have left leaving only one family member in the house to protect it from being broken into and looted. My family has left to [the capital] Sanaa. I had to stay behind to take care of and protect our house.”

Many shop owners have barricaded their stores with bricks to prevent looting. Most restaurants have closed, as have many money lenders, creating a cash-liquidity crisis. The prices of staple goods have soared.

“One of the biggest problems we are facing is a lack of goods and medicines in stores,” said Naji Alrabasi, who heads a labor union. “When I asked some of the owners for the reason, they told me that most suppliers have stopped supplying them. This is one of the reasons why prices have gone up so much.”

On many streets, the rebels have dug trenches and erected sand barricades, preparing for possible street-by-street clashes against the coalition forces, residents said.

Even the province’s deputy governor fled the city.

“I expect more people to leave,” said Hashem Alaz’azi, who spoke from the city of Ibb, where he now lives with relatives. “The people in the city are suffering, and it is expected the suffering will get worse.”

Raghavan reported from Cairo. Karen DeYoung in Washington contributed to this report.