The men were killed on Sunday when their vehicle triggered a mine 400km (250 miles) north of the capital, Colombo, an official said. One soldier was injured.
The official said he believed that Tamil Tiger rebels in Jaffna had planted the mine.
A military official said: "The troops were transporting lunch for their colleagues when they were caught up in the explosion. We believe it is the work of the Tigers."
The official said another soldier was killed in a Tiger attack overnight in the same area.
In other violence, one solider was shot dead on Saturday in northern Sri Lanka while three civilians were killed in the eastern port city of Trincomalee on Sunday.
Sunday's blast was the worst against government troops since they entered a truce with the Tigers in February 2002.
A Norwegian-led truce monitoring panel expressed concern over the latest violence and urged the government and the rebel Liberation Tigers of Tamil Eelam (LTTE) to calm the situation.
"The SLMM warns that there is a real danger that these disturbances and hostilities can spread and result in irreparable deterioration of security"
Sri Lanka Monitoring Mission statement
A statement from the Sri Lanka Monitoring Mission (SLMM) read: "We urge them and all other community leaders to use their influence to ensure that violence and attacks come to an immediate end.
"The SLMM warns that there is a real danger that these disturbances and hostilities can spread and result in irreparable deterioration of security and prevent any real restoration of normalcy in the affected communities."
The statement came after the LTTE put the new government of Mahinda Rajapakse, the president, on notice last month to come up with a solution to the island's drawn out Tamil separatist conflict which has claimed more than 60,000 lives since 1972.
The LTTE said they would begin their campaign for independence next year and set up a homeland unless there was a political settlement to their conflict.
Pressure is on President
Rajapakse to find a solution
The LTTE has been fighting for total independence in the island's northeast, but in December 2002 agreed to settle for extensive devolution of power under a federal system.
In recent weeks, there had been tension in the Jaffna peninsula, the former capital of the Tigers. The situation deteriorated on Friday after the killing of two Tiger rebels by unidentified gunmen.
The LTTE has accused the Sri Lankan military of supporting a breakaway faction. The Sri Lankan military denies the charges.
In the island's northeastern district of Trincomalee, police said they found three bullet-ridden bodies of Tamil civilians on Sunday who had been taken away on Saturday night by Tiger rebels.
They said a fourth man escaped with serious injuries.
Sri Lankan Tamils constitute 12.6% of Sri Lanka's 19.6 million population and Muslims make up 7.5%. The mainly Buddhist Sinhalese are the majority community.