“Every time the sides say ‘cease-fire,’ they start fighting all over again,” said Nabit Muhammed, a taxi driver, standing near houses damaged two weeks ago by a coalition airstrike that killed two people, including a 16-year-old girl, and injured 16. “But we are praying that this time is different.”

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Since the summer, this city on Yemen’s western coast has been at the center of the conflict and of Yemen’s humanitarian crisis, described by the United Nations as the world’s most dire. When the warring sides shook hands on a U.N.-brokered cease-fire in Sweden on Dec. 13, it triggered a collective hope unlike at any other moment during the war.

The challenges were visible during a rare visit to Hodeida last week. After four years of war, suspicion runs deep between the coalition forces backing Yemen’s internationally recognized government and the rebels, known as Houthis. So profound is the animosity that shelling thundered on during the peace talks and in the days after a deal was reached.

“I don’t trust them,” said Moussa al-Qassimi, a wiry 20-something rebel fighter with an AK-47 rifle hanging from his shoulder. “They don’t fear Allah when it comes to bombing civilians. Do you think they will fear Allah when it comes to me?”

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The cease-fire took effect Tuesday, and while both sides appeared to respect it at first, aid workers in Hodeida said Thursday that sporadic shelling and ground fighting had resumed. They said it was too early to say whether the cease-fire was unraveling.

Some of the war’s most pivotal fighting has centered on Hodeida’s rebel-controlled port, a vital entry point for food, fuel, medicine and humanitarian aid bound for the northern part of the country, home to 80 percent of the population.

U.N. and aid agency officials say defusing tensions in Hodeida and restoring the port to full operation could save millions of Yemenis from famine and open the way for a wider peace process.

“If there are signs of progress, for sure it will be a window of hope for the whole country,” said ­Susana Borges, who heads Doctors Without Borders projects in Hodeida.

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Unlike previous cease-fires, this one is propelled by mounting international pressure on Saudi Arabia and its main partner, the United Arab Emirates, to end the war. U.S. backing for the coalition’s military campaign, including logistics and intelligence, has eroded as the result of mass civilian casualties and worsening hunger. The U.S. Senate, dismayed by the slaying of journalist Jamal Khashoggi in a plot blamed on Saudi Crown Prince Mohammed bin Salman, has voted to end U.S. support for the war.

The cease-fire calls for rebel fighters to initially withdraw from the port, leaving the United Nations to oversee its administration. After that, both sides are expected to pull back from the wider city and the province. A joint committee with local forces drawn from both sides will govern the city, and U.N. monitors are to observe and report violations of the agreement. A central road to the capital, Sanaa, will be opened to create a humanitarian pipeline to deliver aid.

As of now, that artery crosses a war zone.

Once known as a vibrant port, exporting dates, coffee and cotton since the Ottoman Turks ruled Yemen in the mid-19th century, Hodeida is now a city of barriers.

Streets are carved up with large shipping containers, huge sand berms and sandbagged firing positions on corners and intersections. Snipers are posted on rooftops, said residents and aid workers.

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In one neighborhood, two days after the handshake deal in Sweden, workers for the rebel authorities were painting murals on shipping containers. One depicted a warship with an American flag firing a cruise missile killing villagers and fishermen. The other depicted torture scenes with a caption alleging the United Arab Emirates, with “American supervision,” was responsible.

On a third container were the words: “We have no choice but confrontation.”

The Houthis, who belong to the Zaidi sect of Shiite Islam, drove Yemen’s government out of Sanaa in early 2015. The Saudi-led coalition of Sunni Muslim countries then entered the war to restore the government and counter the influence of Iran, an ally to the rebels.

The war has killed more than 60,000 people, according to the Armed Conflict Location and Event Data Project (ACLED), a conflict-research group. This year, 37 percent of all civilians killed in Yemen died in Hodeida and its outlying areas, according to ACLED. After coalition forces launched an offensive in June, civilian casualties rose by 160 percent, said the aid agency Save the Children.

Today, Hodeida is a military stalemate. The coalition forces have pushed into the city’s outer edges, surrounding the rebels from the south and the east. Off the coast to the west are Saudi warships. Only one northern road out of the city is accessible to the rebels.

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“Whenever they try, we push them back,” Abu Yasir, a rebel security officer, said near the charred remnants of a tank from a recent battle. “Their dream is to take the port.” Moments later, gunfire erupted from a nearby front line.

More than a quarter of the rebels’ funds come from taxing imports coming through the port, aid workers said. Claiming the rebels bring in shiploads of weapons — which the Houthis deny — the coalition has imposed strict controls on the movements of ships headed to the port.

The success of the cease-fire could determine the fate of thousands of Yemenis in the city who are starving or infected with cholera. Many are too poor or afraid to cross front lines, often laced with land mines, to access ill-equipped hospitals. The city was once home to 600,000 people, and now nearly two-thirds have fled. Few have returned.

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Restaurants and shops remain open downtown, and traffic is congested. But in other areas, streets are empty and covered with trash. Cars with flat tires have been abandoned, if not stripped for spare parts.

Many people who are too poor to escape — or tried and failed — remain.

“We ran out of money,” said Amran Mansour, a fisherman who fled two months ago. “We were forced to come back.”

U.N. officials fear thousands more could die of cholera, hunger or in the crossfire of house-by-house urban warfare if the cease-fire fails.

Already, residents routinely die.

Two days after the peace talks began, a shell crashed into Ahmed Hathim’s home in the city’s Rabasa enclave. It instantly killed his 5-year-old grandson and 17-year-old daughter and injured seven more of his relatives. Hathim said he couldn’t tell which side fired the mortar.

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At Al Thawra Hospital, his ­25-year-old daughter, Wafa, had her leg amputated. She had recently graduated with a nursing degree and had been looking for a job.

“She was the first member of our family to go to university,” said Hathim, weeping. “Now, what is her future going to be like?”

In the hospital’s cholera ward, 15 to 20 patients arrive each day. Roughly half test positive, mostly the result of poor sewerage and lack of water-treatment facilities, said Entessar Ahmed of the aid agency Action Against Hunger, which operates the ward.

Last month, clashes erupted outside the hospital, forcing hundreds of patients and staff members to run for cover, dodging bullets and shrapnel, staffers said. “We hope the cease-fire works and peace comes through,” said Ahmed. “We fear for our lives.”

Behind the hospital is a fish market that was bombed last year. Boats idle in the water because many fishermen are too afraid to go out to sea. They recounted being shot at by coalition warships and helicopters. Some had shrapnel wounds and other injuries. One fisherman recalled how he was arrested by the coalition and held for two months. More than 25 fishermen are still in the coalition’s custody, accused of being Houthi fighters, community leaders said.

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A coalition spokesman did not respond to a request for comment.

“These days, only those who have courage go out to sea,” said fisherman Mazem Ahmed, 20, as others around him nodded in agreement.

At the port, Houthi officials and their fighters said they will leave it only if coalition forces end airstrikes and withdraw from the city first. One fighter vowed to “fight until the end.”