A pair of weary brothers walked through San Francisco International Airport until they were met, at a full sprint, by a third brother who wrapped his arms around them, smiled and exclaimed, “I missed you!”

This was no ordinary arrival.

The scene, Wednesday evening, was the culmination of an ordeal that saw the brothers from central California — Yassin and Mohamed Mohsen — trapped in their family’s war-torn homeland of Yemen before a harrowing, improbable escape on a boat made for ferrying animals.

Their journey highlights the plight of scores of Yemeni Americans who were in the country in March when violence escalated between rebel Houthi forces and those aligned with the exiled president, Abd-Rabbu Mansour Hadi, who were backed by a fierce, Saudi-led air campaign.

The United Nations estimates that nearly 2,300 people have died in the war and that 80 percent of the population needs humanitarian aid.

Some advocacy groups have pushed the U.S. to help its citizens still stuck in the country, but the State Department — which has long warned Americans not to travel to Yemen — has said a military intervention could put civilian lives at greater risk.

“It's troubling that Yemeni Americans remain trapped in a war zone, without any support from the United States,” said Zahra Billoo, who directs the Bay Area chapter of the Council on American-Islamic Relations, which sued Secretary of State John Kerry and Defense Secretary Ashton Carter in hopes of spurring action.

That debate was far from the minds of Yassin Mohsen, 19, and Mohamed Mohsen, 11, as they threw their luggage in Jaffar Mohsen’s truck late Wednesday and headed home to Firebaugh (Fresno County).

The brothers were at once relieved and fearful. Two sisters, ages 7 and 8, as well as a 21-year-old brother and their mother, remain trapped in Yemen.

“It feels — I don’t know what’s the word — but it feels great to be home,” Yassin said. “I’m safe here now.”

The family — which runs grocery stores and restaurants in Fresno and Madera counties — had traveled to Yemen in February for a wedding, but couldn’t leave.

During his four months in the country, Yassin said he witnessed horror after horror — bodies in the streets, children holding guns and and shooting them into the air, a burned skeleton in a car that had been gutted by a rocket.

One night, he said, an air strike took out a police station near the house in the city of Aden where the family hid with little electricity, water and propane, and the flames lit up the neighborhood. His loved ones ran for the basement.

“I was already thinking, ‘I’m probably going to die here,’” Yassin recalled.

Yassin’s father escaped first, jumping on an Indian naval ship in April off the coast of Aden. In a chaotic rush, though, the rest of the family was left out as scores of people piled into fishing boats heading for the larger ship.

In late May, Yassin said, he and his brother made what was their third trip to the water, and managed to secure a spot on a boat — one typically used to ship animals — that traveled across the Gulf of Aden to the small country of Djibouti on the Horn of Africa.

The entire family had been previously denied twice at Aden’s port. This time, Yassin’s mother decided to stay home with three of the siblings, due to the danger of the trek, and wait to see how Yassin and Mohammed would fare.

The boat was packed, the brothers recalled, with about 300 people lined up so close they couldn’t move. Yassin said he didn't turn on his phone for fear of alerting snipers. Word had spread of another boat being attacked.

Women fainted, children screamed, and many passengers vomited as the ship drifted through the night. Rats and cockroaches scurried across the floor. There was no water or food.

“I was just talking to myself: ‘What if this happens, what if that happens?’” Yassin said. But I was trying to keep myself calm because I had my little brother and I didn’t want him to get scared.”

Fourteen hours later, the brothers made it to Djibouti. But their trouble wasn’t over yet.

Local officials wouldn’t allow them to leave the port — and they confiscated Yassin’s passport — so the pair sat and slept on a dirty mat for nearly two days, in the scorching heat.

Nearly 600 people had arrived from Yemen the same day, Yassin said. He pleaded with port officials — “I’m an American citizen!” — but they told him to go away, answering, “This is not America.”

American officials came to the port, he said, took down his information and returned the next day to help release them.

For the next two weeks, the Mohsen brothers waited in Djibouti, which was full of refugees, as their passports were processed. They slept on the roof of a hotel, paying $120 a night for the use of two mattresses.

Finally, they boarded a flight home.

In California, 31-year-old Jaffar Mohsen had spent countless nights wondering if his brothers would emerge alive. On Wednesday, he waited nervously at the airport — checking his phone, tapping his shoes, incessantly adjusting his gray hat and whispering under his breath as he sat at the very edge of a seat.

“I’m practicing what I’ll say to them,” he said.

He thought back to the text messages Yassin had sent him every morning in May, telling him he loved him in case he died.

“It’s almost unbelievable. To this moment I’m still shocked that I’m going to be able to see them,” Jaffar said. “This is one of the most exciting moments of my life.”

When he saw his brothers, he took off running.

But the joy of the reunion was tempered by worry about the rest of the family, still surviving in a war zone.

“I wish we were one big family,” Jaffar said. “Why am I so excited if they’re not all here? I’m thinking about my other brother, sisters and my mom. I feel guilty being happy for just a small part of my family.

“But I still have hope and faith,” he said, “that they will be back here again and we will live again as a nice, happy middle-class family. ”

Hamed Aleaziz is a San Francisco Chronicle staff writer. E-mail: haleaziz@sfchronicle.com Twitter: @haleaziz