Prime Minister Kim Hwang-sik and scores of political and military officials were among some 500 people at the funeral for Staff Sgt. Seo Jeong-woo, 22, and Pvt. Mun Gwang-wook, 20, the Yonhap news agency said.
The soldiers and at least two civilians were killed Tuesday when North Korean shells rained down on the island of Yeonpyeong, home to a South Korean military base.
Saturday, hundreds of Korean veterans, some former special forces troops, faced off with riot-equipped police at a rally in downtown Seoul calling on the government to retaliate against North Korea for shelling the island, the Canadian Broadcasting Corp. said.
Demonstrators burned a North Korean flag, sprayed officers with fire extinguishers and beat some with wooden stakes when police pushed back with the shields.
North Korea said the shelling was to deter South Korea from conducting military exercises from its base in the disputed area near the border.
In his eulogy, marine Cmdr. Yoo Nak-jun vowed revenge for the soldiers' deaths.
"We will pay back North Korea 100 times, 1,000 times for atrociously killing and wounding our soldiers, who were the pride of the marines," he said.
The ongoing South Korean military exercises will continue on a larger scale when the aircraft carrier USS George Washington arrives in the Yellow Sea to participate, which North Korea said it considers an act of aggression, the report said.
Gen. Walter L. Sharp, commander of U.S. forces in South Korea, went to Yeonpyeong Island to survey the damage from Tuesday's bombardment, The New York Times reported. Soon afterward, artillery blasts could be heard, but the rounds didn't fall in South Korean territory, the Times said.
Kwon Ki-hyeon, a spokesman for the South Korean Defense Ministry, surmised the shots had been part of a drill or perhaps an effort to frighten South Korean troops on the nearby island where most of the 1,600 civilian residents have fled.