The pair were killed on Thursday in Polonnaruwa
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Sri Lanka's government has accused Tamil Tiger rebels of breaking the ceasefire by killing an intelligence officer and an informant.
It said the killings cast doubt on the rebels' commitment to peace.
The two men were shot by gunmen on a motorcycle in the town of Polonnaruwa in eastern Sri Lanka.
In a BBC interview on Thursday, President Chandrika Kumaratunga urged the rebels to compromise and return to peace talks that broke down last year.
'Hallmarks'
Army corporal Ajith Dassanayake and Vasanthanayagam Prabhakaran, a Tamil civilian, were gunned down on Thursday.
No group has yet said it carried out the shooting but the government said in a statement it "bears the hallmarks of the [Tigers]".
Mrs Kumaratunga has urged the rebels to return to talks
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"This is a direct violation of the ceasefire agreement, which calls on the parties not to engage in assassinations."
The ceasefire has largely remained intact since February 2002, even though the Tigers pulled out of negotiations in April last year, saying the government was not honouring pledges it had made for the north and east.
The Tigers have been fighting for more than two decades for self-government.
The most recent threat to the ceasefire came in July when a suicide bomber killed four policemen in Colombo.
The Tigers denied involvement but correspondents said there was little doubt of their responsibility.
Speaking to the BBC on Thursday, Mrs Kumaratunga appealed to the rebels to restart talks, saying she had done as much as she could to come to the negotiating table.
She said she was willing to discuss the Tamil Tigers' proposal for interim self-rule and also a long-term federal solution.
She said she had moved 75% of the way towards the rebels' position and accused the Tigers of not compromising at all.
A recent statement on a pro-rebel website accused the president of deceit and cheating the international community.
Since the talks stalled last year a number of attempts by Norwegian mediators have failed to restart the process.