member of the Saudi security forces was killed and an armed suspect gunned down during a clash in an eastern neighbourhood of Riyadh on Monday evening.
Four other police officers were wounded during the shootout in Al-Rawabi neighbourhood, which was cordoned off as police tried to track down another three suspects who fled, said the statement.
"One member of the security forces, and one of the militants they were chasing, were killed," one witness told AFP.
"Security forces are combing the area, but the exchanges of fire have died down," the witness said three hours after the clash began.
"A confrontation between security patrols and a group of wanted militants began at 6:30 pm (1530 GMT)," a resident of Al-Rawabi earlier told AFP.
"Heavy gunfire is being heard as well as blasts apparently resulting from rocket-propelled grenades (RPGs) and hand grenades," he said.
Dozens of police cars were seen speeding to the area, an AFP correspondent reported.
Security forces blocked off access to the neighbourhood, keeping crowds of curious onlookers out.
The last of a series of gunbattles between security forces and presumed Islamist fighters occurred in the Saudi capital a week ago.
Security forces gunned down a militant and wounded another on 5 April, also in an eastern district of Riyadh.
Both were wanted on terror-related charges, but neither was on a list of 26 most-wanted suspects, which has gone down to 22 since it was issued in December, after a series of human bombing attacks targeting residential compounds that killed 52 people in May and November 2003.
Saudi authorities have waged a relentless crackdown on suspected sympathizers of al-Qaida terror network since the bombings.
Many suspects, as well as security personnel, have been killed in clashes, particularly in Riyadh.
Hundreds more presumed extremists have been rounded up across the vast kingdom, and authorities have reported seizures of huge caches of weapons and explosives, including hundreds of explosive belts.