(Reuters) -- A U.S. military instructor helping train Yemeni coast guards was shot and seriously wounded in an attack by unidentified assailants in the Red Sea city of Hudaida on Sunday, a Yemeni security source said.

The source said two other U.S. instructors, who were travelling in the same car, were not hurt in the attack, which happened before noon on the group's journey to work.

A caller told Reuters by telephone - not the group's usual method of communication - that the al Qaeda-linked Ansar al-Sharia group was behind the attack. The authenticity of the claim could not immediately be verified.

The gunmen were traveling by car and they hit one of the Americans and his condition is serious, the Yemeni security source said. He said the two other men were unhurt.

Officials at the U.S. Embassy in Sanaa said they were checking the report.

U.S. military instructors are helping train the Yemeni armed forces, who are waging a battle against al Qaeda-linked militants in southern Yemen, seen by the United States as a major threat to its security.

The attack was the latest in a series of security incidents in Hudaida over the past two months.

In March, a Swiss woman was kidnapped at gunpoint in Hudaida as she left a privately owned language institute where she taught English. She said in a video posted online earlier this month that she was being held by al Qaeda militants and asked Swiss authorities to help secure her release.

In April, a French official of the International Committee of the Red Cross was also kidnapped while traveling from northern Yemen to Hudaida.

A tribal source later said he had been transported to the southern town of Jaar, an Islamist militant stronghold, where he is still being held.

(Reporting by Mohammed Ghobari; Writing by Sami Aboudi; Editing by Louise Ireland)