During an interview in his office here, Mr. Omgy acknowledged that his company had provided financial services to Al Qaeda. “We had no other option but to comply with them,” he said. “They were the rulers of the city.”
But he denied the Treasury Department’s charge that he was a Qaeda member, describing his ties to the group as a business relationship that had ended. “They withdrew their money before they left the city,” he said.
The case of the Omgy brothers is a small but telling account of the chaos that has engulfed Yemen, the southernmost country on the Arabian Peninsula and the Arab world’s poorest state.
Since 2011, when protests erupted against the previous president, Ali Abdullah Saleh, much of the state has collapsed, and armed tribes and militias have taken control of significant territory. In 2014, rebels from the north known as the Houthis stormed the capital, Sana, forcing the government into exile and dividing the country.
The Houthis now control the northwest, including the capital, where they have struggled to exert authority over what remains of the government. Much of the south and east are held by forces backed by Persian Gulf nations and are nominally loyal to the exiled president, Abdu Rabbu Mansour Hadi.
So much upheaval has often left Yemenis, struggling to meet their needs, to deal with whichever armed group has most recently taken control.
And so it was in April 2015, when Qaeda fighters seized a chunk of territory along Yemen’s southern coast — and turned to the Omgy brothers for their banking needs.
Mr. Omgy was so upset by the charge against him that he invited an employee of The New York Times to his office in Al Shihr to tell his side of the story.
His headquarters bore testament to the business’s success, with green marble floors, comfortable sofas and central air-conditioning — a luxury in a country where millions struggle to find enough food, much less power to charge their phones. Three new Lexus sport utility vehicles were parked outside.
The brothers opened their first money exchange in 1990 and now have 95 offices across Yemen that work like banks, holding accounts and performing inexpensive money transfers, Mr. Omgy said.
“I received the news from social media and news sites,” Mr. Omgy said of the Americans’ designation of him as a Qaeda member. “I have never financed Qaeda activities nor joined the organization.”
He did, however, acknowledge doing the group’s banking.
After the militants seized the area, the brothers closed their offices, he said, but reopened because none of the banks would. The local branch of Yemen’s national oil company maintained an account, as did the civilian council that helped run local affairs. Even the government relied on the company to get salaries to its employees, according to Yemeni officials.
The United States said in its designation that a Qaeda official in charge of taxation had held an account with Al Omgy from which he sent money to militants around Yemen. It also said that early this year Al Qaeda ordered the oil company to transfer more than $1 million to Al Omgy “to support terrorist activities.”
Mr. Omgy said he had been forced to give the militants accounts.
“We opened the accounts when they threatened us,” he said. Then, to pay their taxes, the oil company and local businessmen would ask Al Omgy to transfer money from their accounts to those of Al Qaeda.
He denied that the company had paid Al Qaeda a 10 percent commission on all transactions, as the United States also charged, but said that individual Qaeda members could have transferred money through the company.
“We have branches everywhere,” he said. “We could not reject their orders.”
He dismissed the rest of the United States’ charges, that he had smuggled arms for Al Qaeda and that his brother had raised funds for the Iraqi insurgency.
“I have neither political nor religious affiliations,” he said.
Staying open had been the only way the company could provide services for others, he said, including the Yemeni government, which the United States considers an ally against Al Qaeda.
“The government asked us to turn to Al Omgy,” said Saeed Bahmran, who works for the Education Ministry in Al Mukalla, a nearby city also seized by Al Qaeda. “Al Omgy has branches everywhere, and we can get our salaries at anytime, even at midnight.”
Mohammed Sharem, the director of the local branch of the national oil company during Al Qaeda’s control, said, “Our relationship with Al Omgy is strong and it is an excellent company.”
He said government-owned gas stations deposited their profits directly into the oil company’s account with Al Omgy, and kept doing so after Yemeni forces pushed Al Qaeda out in April 2016.
After the designation, the governor of Hadramawt Province blasted the decision in a statement, saying the Omgy brothers had “stood with the sons of the province during the hardest and most complicated times.”
Mr. Omgy is unsure how the designation, which the Americans made in cooperation with the United Arab Emirates, will affect his business, as he has no assets in either country. But he is looking for ways to challenge a decision that he says has tarnished his name.
Its effects may have already hit others.
A soldier with the local force supported by the United Arab Emirates in southern Yemen said that so many of his colleagues used to get their salaries through Al Omgy that the company would deliver the cash to their base to prevent backups at its branches.
But last month, their pay did not come.
“This is the first time they haven’t paid our salaries,” said the soldier, who spoke on condition of anonymity for fear of being associated with a company associated with Al Qaeda.