Sana'a Gunmen on a motorbike on Sunday killed a US teacher in Yemen's second city of Taez, an official said, just days after suspected Al Qaida militants kidnapped a Swiss female teacher in the country.

The assailants opened fire on the man, who was the deputy director of a Swedish language centre in the city 270km southwest of Sana'a, the security official told AFP on condition of anonymity.

The victim was in his car in the neighbourhood of Sena, he said, adding the gunmen fled the scene after the shooting.

The US embassy in Sana'a said it did not have any information about the killing and that it was investigating the report.

Another security official said the attack appeared to be the work of Al Qaida.

"It carries the fingerprints of Al Qaida, but investigations are ongoing" to identify the culprits, the investigating officer said, asking not to be named.

The United States says the Yemen-based Al Qaida in the Arabian Peninsula, or AQAP, is the most active branch of the global terror network.

Witnesses said however that the attackers were dressed in the uniform of the elite Republican Guard, led by the son with former president Ali Abdullah Saleh, Ahmad.

Opponents of Saleh have repeatedly called for the command of the military to be purged of relatives of the veteran leader, who was forced to step down last month after year-long protests inspired by the Arab Spring.

The attack comes two days after an official said suspected Al Qaida gunmen abducted a Swiss woman, also a teacher at a language school, in the Red Sea port of Hodeida and moved her to the restive province of Shabwa further to the east.

The Swiss foreign ministry confirmed the abduction and said it had been informed the woman had been kidnapped late Wednesday and were trying to seek her release.

Al Qaida militants have exploited the weakening central government in Sana'a to strengthen their presence in the country, especially across the restive south and southeast.

In other violence on Sunday, missiles fired from the sea slammed into Al Qaida positions in the southern city of Zinjibar, killing at least 16 suspected militants, a local official said.

He said the heavy shelling began overnight targeting the northeastern suburbs of Zinjibar, which jihadists have controlled since May following fierce fighting with government troops.

Al Qaida's local branch is active in the south and east of Yemen, but not in Taez, which was a major centre for the opposition movement that eventually forced former president Saleh to step down.

More than 200 people have been abducted in Yemen during the past 15 years, many of them by members of the country's powerful tribes who use them as bargaining chips with the authorities.

Almost all of those kidnapped were later freed unharmed.