South Korean President Lee Myung-bak has ordered his air force to attack North Korea's missile bases if his country is further provoked, after artillery shells killed two of the South's soldiers and sparked a deadly retaliation.

World leaders have spoken out against the burst of violence, including Prime Minister Stephen Harper, who condemned the North's artillery attack.

"This is the latest in a series of aggressive and provocative actions by North Korea, which continue to represent a grave threat to international security and stability in northeast Asia. Canada will continue to condemn all acts of aggression by North Korea in violation of international law," Harper said in a statement.

"On behalf of all Canadians, I extend my condolences to the families of those who were killed and injured as a result of this unprovoked attack."

Harper urged North Korea to "refrain from further reckless and belligerent actions."

The conflict apparently began with a warning from North Korea, ordering the Seoul government to cease military drills in disputed waters. Seoul acknowledged that it fired two shots in the area, but said they did not land in the North's territory.

When the South continued its military activities, North Korea began bombarding South Korea's island of Yeonpyeong with artillery fire.

In Yeonpyeong, which lies only 11 kilometres from the North Korea mainland, the incoming fire set buildings ablaze and left hundreds of civilians fleeing for their lives. At least three civilians and 16 South Korean soldiers were injured.

Yeonpyeong resident Lee Chun-ok said the shelling began when she was watching TV in her home. A wall and a door in her home collapsed during the attack.

"I thought I would die," Lee said Tuesday, after being evacuated to the port city of Incheon. "I was really, really terrified, and I'm still terrified."

South Korea responded to the attack by scrambling fighter jets and firing howitzers. Its officials said there could be considerable damage to North Korean targets, though there was no information on casualties from the North Korean side.

The clash lasted about an hour. When it was over, each side said they would not tolerate further aggression.

Lee said his country would not tolerate an "indiscriminate attack" on civilians.

"Enormous retaliation should be made to the extent that (North Korea) cannot make provocations again," he said.

In North Korea, the Pyongyang supreme military command said that if the South crossed the maritime border by "even 0.001 millimeter," there would be further strikes.

An official statement from North Korea indicated that it had been "reacting to the military provocation of the puppet group with a prompt powerful physical strike."

And North Korea accused the Seoul government of inciting the clash through "reckless military provocation as firing dozens of shells" inside the North's territorial waters.

The United States quickly declared its support for South Korea, where it has 28,000 of its own troops stationed.

White House spokesperson Robert Gibbs called on North Korea to "halt its belligerent action and to fully abide by the terms of the armistice agreement," the pact that ended the Korean War in 1953.

Canadian Foreign Affairs Minister Lawrence Cannon also urged North Korea to remain faithful to the terms of the armistice agreement, and suggested that North Korea was fully aware that South Korea was scheduled to conduct a training exercise on Tuesday.

"These actions continue to pose a grave threat to the region and to the entire world," Cannon told reporters on Parliament Hill. "We are in touch with the Canadian embassy in Seoul and are monitoring the situation closely."

Cannon said no Canadians were injured in the incident, and none requested consular assistance.

Cannon said he is urging the United Nations Security Council to "get active on this file" and "condemn North Korea for these actions."

Experts said the clash was a reminder that the unpredictable North Korea regime remains a security threat.

Fen Hampson, director of the Norman Patterson School of International Affairs at Carleton University, said the conflict was likely linked to North Korea's internal politics. Kim Jong-il recently promoted his youngest son, Kim Jong-un, to a four-star general, making him his likeliest successor.

"We are seeing the beginning of a regime change," he told CTV's Power Play. "This is really activity that we've seen before. In 1987, the (North) blew up a South Korean airlines. Earlier this year in March, they sank a South Korean warship. These are what I would call inevitable but dangerous antics, that come from an embattled regime where we're also seeing a major leadership transition."

Paul Stares, Senior Fellow for Conflict Prevention and Director of the Center for Preventive Action, said it's likely an overstatement that "we are on the brink of another Korean war," but there is great concern tensions could be further escalated.

However, he cautioned "there is still significant risk of unintended escalation."

"I worry that through miscalculation, misunderstanding, miscommunication, that things could get a lot worse," said Stares.

The deadly clash on Tuesday was not the first time that Yeonpyeong had been dragged into the perpetual conflict between the two dies.

In June 2002, a South Korean warship sank and six sailors died in waters around the island. North Korea said it suffered an undisclosed number of casualties in the same incident.

Seven years later, South Korea reported that a clash killed as many as 30 North Koreans and wounded several South Koreans sailors.

With files from The Associated Press