At least 50 other people were injured in the port town of Trincomalee when a bomb fixed to a bicycle exploded, hours after a Claymore fragmentation mine killed two constables in the same district, police said.
An indefinite curfew was clamped on the area as rioting erupted after the market blast.
At least seven shops were torched and several vehicles damaged, police said.
The government blamed the rebel Tamil Tigers for the blasts.
There was no comment from them.
Thirty-four people have now been killed in four blasts since Monday, dimming hopes for talks slated for next week between Colombo and Tamil Tiger rebels in Switzerland to save their tottering ceasefire.
The Dutch government, on behalf of the European Union, condemned the latest violence and urged the parties to honour pledges made during talks in Geneva in February to uphold the February 2002 truce.
"Recent violent incidents illustrate a flagrant disregard for the commitments made by the parties at Geneva and place in seri