In recent years, Yemen has been locked in a war between the Houthis in the north and forces nominally loyal to the internationally recognized president in the south.
Since 2015, Saudi Arabia and a coalition of Arab countries that back the president have been bombing Houthi-controlled areas to try to restore the president to the capital, contributing to a large humanitarian crisis.
No group immediately claimed responsibility for Mr. Burch’s abduction, and it remained unclear why he was taken.
Mr. Burch had been living in Yemen for years and working as an engineer for Safer, a state-owned oil company. He had converted to Islam, married a Yemeni woman and had three children, ages 7, 9 and 12, according to his wife and colleagues.
His American passport said he was born in Louisiana, and his wife said he had been living in Texas. His LinkedIn page said he had graduated from Kilgore College in Kilgore, Tex., and held numerous jobs in the oil industry in Texas and in Yemen.
He had most recently worked as a mechanic and cement technician at Safer, the page said.
Ms. Forsa said her husband had left home on Sunday morning to take their sons to a sports club. When he did not return, she called him and found that his phone had been turned off. She called the club, and then his office, but no one knew where he was.
“I knew that something was wrong,” she said.
The police later told her that witnesses said he had been stopped on a busy street in Sana by five armed men in civilian clothes who drove a pickup truck with no license plates.
After they took Mr. Burch away, two of them parked his car on a side street, where Ms. Forsa later found it, she said.
“When I saw the car, my heart fell,” she said.
She told the couple’s sons that their father was traveling and that she looked upset because he had not informed her ahead of time. “I don’t want to ruin their lives,” she said.
The abduction took place in a part of Yemen that is tightly controlled by the Houthis and where Al Qaeda is not believed to have an active presence.
Ms. Forsa said she did not know who had taken her husband. “We don’t know who is behind this,” she said.
A Yemeni security official and two of Mr. Burch’s colleagues at the oil company confirmed the account, speaking on the condition of anonymity because they were not authorized to speak to journalists.
A spokesman for the United States Embassy to Yemen, currently based in Jidda, Saudi Arabia, said it could neither confirm nor deny the kidnapping.
The United States’ State Department has warned American citizens against traveling to Yemen because of “the high security threat level posed by ongoing conflict and terrorist activities.”
In recent years, rebel groups in Sana have “systematically detained U.S. citizens,” many of whom are not allowed to communicate with their families or consular officials, the department says on its website.
It also says the United States government has limited ability to help those in detention because embassy operations were suspended and its American employees removed from the country in February 2015.
In 2015, a Frenchwoman working on a project with the World Bank was abducted with her Yemeni interpreter near Sana. Both women were released later that year.
In 2014, American commandos raided a village in southern Yemen to try to free an American held by Al Qaeda’s regional brach, Al Qaeda in the Arabian Peninsula. But the hostages — Luke Somers, an American photojournalist, and Pierre Korkie, a South African teacher who was being held with him — were killed by their captors when they realized that a rescue attempt was underway, United States officials said.
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