The injuries occurred when a parcel bomb exploded as a police vehicle drove by in Trincomalee town, police said, wounding four constables and two civilians.
Stores closed and the streets quickly emptied as panic-stricken shoppers fled, residents said.
Police also said that a constable travelling in a bus was shot dead by a gunman thought to be from the rebel Liberation Tigers of Tamil Eelam (LTTE) group.
The violence came after long-range artillery battles in the northern peninsula of Jaffna halted Monday, defence ministry spokesman Prasad Samarasinghe told reporters.
He said 35 troops were killed in the fighting which erupted Saturday while about 130 soldiers were wounded.
He claimed the military killed at least 150 rebels, but managed to recover only 11 bodies.
"We have moved about 800 meters (874 yards) ahead of our defences and we are now consolidating," Samarasinghe said. "There is no major fighting now.
We have neutralised the Tiger gun positions ahead of our defences.
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