Six men travelling in two three-wheeler taxis were shot dead by security forces when they tried to attack a military sentry point at Nelliyadi in the Jaffna peninsula, military officials said.
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More than 60,000 people have been killed in the island's separatist conflict in the past three decades.
Some 200 people have been killed in the past month, the bloodiest period since a 2002 truce took effect between Tamil Tiger rebels and the government.
The two policemen died in a grenade attack in Vavuniya district where a mine blast was also reported, said police officials in the region, 260 kilometres (160 miles) north of Colombo.
The latest violence came two days after gunmen stormed the offices of the Uthayan newspaper in Jaffna and killed a manager and another employee.
Six people arrested in connection with the attack were freed on bail Wednesday.
Last week a suicide bombing in Colombo critically wounded army chief Sarath Fonseka and killed 11 others including the bomber.
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The government, saying it was acting in self-defence, retaliated with air strikes against suspected positions of the Tigers, who are fighting for a separate state for minority Tamils.