Amnesty International has urged the Sri Lankan government to investigate fully a spate of killings of civilians.
Relatives mourn Tamils killed near Jaffna
The human rights group noted "a disturbing pattern of incomplete or ineffective investigations by the government" into such violence.
The appeal came after 13 Tamil civilians, two of them young children, were shot dead near Jaffna on Saturday.
Tamil Tiger rebels accused the navy of "slaughter", but officials denied any involvement and blamed the rebels.
The two sides have failed to agree dates for fresh peace talks in the past month, which has seen more than 200 people killed, many of them civilians or members of the security forces.
Last week, international ceasefire monitors repeated that they had evidence to suggest the authorities were involved in killing Tamils, although not in a systematic way.
Sri Lanka's authorities reject suggestions they are in any way involved in the killings.
Meanwhile, at least two civilians and three members of the security forces were killed in a series of attacks in the north and east on Wednesday.
A four-month-old baby, his four-year-old brother and their parents were among those shot dead on Saturday night on navy-controlled Kayts island near the northern town of Jaffna.
Amnesty International said it was alarmed by the increasing number of civilians being killed in what it called a "low-intensity armed conflict" in Sri Lanka.
The group welcomed the government's condemnation of the Kayts island killings and the announcement that police were investigating.
But it added: "There is a disturbing pattern of incomplete or ineffective investigations by the government, with the result that perpetrators of such violence generally operate with impunity.
"The government must carry out independent, impartial and effective investigations into all killings; the results of these investigations should be made public, and those found responsible for the attacks must be brought to justice."
Amnesty said it had received "credible reports" that Sri Lanka navy personnel and gunmen affiliated with the Eelam People's Democratic Party (EPDP), a Tamil political party opposed to the Tamil Tigers, were present at the scene of the killings.
"Regardless of who is responsible for the attacks, the Sri Lankan government has obligations under international law to take steps to prevent such killings," it said.
EPDP secretary-general Douglas Devananda dismissed the suggestion as "baseless".
"There is no link between the EPDP and the incidents in northern Sri Lanka," he told the BBC Tamil service.
The Tamil Tigers said the navy or paramilitary groups supported by the security forces killed the Tamils on Kayts.
The government suggested the killings could be a part of a rebel strategy "to divert international opinion", but the rebels said they had no access to the area.
A 2002 truce accord is under severe strain but is still technically in place.