The government said the fighting broke out when two policemen tried to check on a suspected Tamil Tiger rebel.
He was at a tea kiosk near the Ceremonial Drive that leads to the national parliament building.
The constables were killed and later one of the rebels detonated explosives strapped to his body.
Several of his colleagues exploded grenades and fired indiscriminately at vehicles trapped in the evening rush-hour traffic.
Reports said several people were caught in the cross-fire.
Police said the attackers, believed to be members of the Liberation Tigers of Tamil Eelam (LTTE), also fired rocket-propelled grenades along the highway that is used by ministers and legislators to return from parliament.
Nimal Gunatilleke, a top police official, said he believed the attackers may have been lying in wait for Deputy Defence Minister Anuruddha Ratwatte, who had been due to take that route after a parliamentary debate.
One of the minister's advance security vehicles was hit by a grenade. The minister, who was not in the vicinity at the time of the attack, has been co-ordinating the war against the Tigers.
Security personnel gunned down two of the attackers, including a suicide bomber, and commandos defused the explosives strapped to him.
A gun battle followed as several other rebels fled the area by detonating at least four other bombs or grenades.
The government said that security forces were conducting a cordon and search operation in the area, to locate the Tigers who escaped.
Police said many of the wounded were in a critical condition in hospital, and fatalities were expected to rise.
Suicide bombers
Previous attacks in the capital have been blamed on the LTTE, who are fighting for independence in the north-east of the island.
The group has been accused of several suicide attacks against politicians and the military.
In January, a woman suicide bomber detonated explosives strapped to her body outside the prime minister's office, killing at least eight people.
The previous month, President Chandrika Kumaratunga narrowly escaped assassination when a suicide bomber attacked a meeting she was holding.
A total of 26 people attending the meeting were killed, but she escaped with a wound to her right eye.
Peace efforts
The latest attack came amid efforts to organise peace talks between the government and Tamil Tiger rebels, with Norwegian mediation.
President Kumaratunga held a meeting this week with the main opposition leader, Ranil Wickramesinghe, to discuss a proposed package which would allow more autonomy for Tamil areas of the country.
It is hoped that, once there is cross-party agreement, the Tamil Tigers can be persuaded to consider the package.
Over 55,000 people have been killed in the civil war over the past two decades.
Related to this story:
Sri Lanka peace meeting hits snag
(21 Feb 00 | South Asia)
Analysis: Fifteen years of bloodshed
(18 Dec 99 | South Asia)
What chance peace in Sri Lanka?
(23 Feb 00 | South Asia)
Tigers release four captives
(28 Feb 00 | South Asia)
Fighting overshadows peace mission
(15 Feb 00 | South Asia)
Fighting escalates in Sri Lanka
(01 Jan 00 | South Asia)
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