Updated

Saudi security forces battled heavily armed suspected Al Qaeda (search) members holed up in a sea-front apartment building Monday, a day after two militants — one of them the kingdom's No. 3 most-wanted terrorist — died in clashes across this eastern city.

Zaid Saad Zaid al-Samari (search), a 31-year-old Saudi, was killed during fighting Sunday in Dammam, a security official said, speaking on condition of anonymity because he was not authorized to give information to the media. A police officer also was killed Sunday.

Al-Samari was on a list of 36 most-wanted terrorists sought in relation to multiple terror attacks launched in this kingdom since May 2003.

An unknown number of militants fled Sunday to a white two-story building near Dammam's commercial district, which police surrounded on Monday as fierce gun battles continued for a second day.

Officers evacuated people from nearby buildings and cordoned off streets leading to the area, including the city's main coastal promenade. Sporadic gunfire could be heard as police helicopters circled overhead.

The clashes prompted U.S. authorities to close the American consulate in nearby Dhahran (search).

The Interior Ministry said Sunday that security forces were fighting "a number of elements affiliated to the 'deviant group"' — a term usually used in reference to Al Qaeda's branch in the kingdom.

Since May 2003, Islamic militants have carried out numerous suicide bombings and kidnappings and regularly battled security forces. The attacks, which have tended to target Westerners and housing complexes were they live, have been blamed on Al Qaeda and its allies.

Al Qaeda wants to topple the Saudi royal family because of its close ties with the West, particularly the United States.

Saudi leaders say they have gotten the upper hand against terror cells, killing or capturing all but one figure on a previous most-wanted list of 26 militants.