SEOUL, South Korea — Hours after North Korea’s deadly artillery attacks Tuesday, South Korea’s president said “enormous retaliation” is needed to stop Pyongyang’s incitement, but international diplomats urgently appealed for restraint.

“The provocation this time can be regarded as an invasion of South Korean territory,” President Lee Myung-bak said at the headquarters of the Joint Chiefs of Staff here, according to South Korea’s Yonhap news agency.

The incident — in which two South Korean marines died — is “the first direct artillery attack on South Korean territory since the Korean War ended in an armistice, not a formal peace treaty” in the 1950s, South Korea’s Yonhap news agency reported.

Scott Snyder, director of the Center for U.S.-Korea Policy, a program of the Asia Foundation, called the act a “very serious provocation” and said it was “unprecedented in recent years [at least since the 1970s if not longer] in terms of artillery beyond the DMZ into civilian areas.”

The United States has about 28,500 troops deployed in South Korea who are warily watching the situation. A U.S. defense official said there are “more than 50 U.S. Navy vessels in the area, including a carrier strike group led by the USS George Washington. However, there are no plans to send more ships or forces in response to the strike.

Along with the slain marines, 15 South Korean soldiers and three civilians were wounded when the North fired about 100 rounds of artillery at Yeonpyeong Island in the Yellow Sea, South Korea authorities said. The attack also set houses and forests on fire on the island.

South Korea’s military responded with more than 80 rounds of artillery and deployed fighter jets to counter the fire, defense officials said.

Firing between the two sides lasted for about an hour in the Yellow Sea, a longstanding flash point between the two Koreas. In March, a South Korean warship, the Cheonan, was sunk in the area with the loss of 46 lives in a suspected North Korean torpedo attack.

Lee called “indiscriminate attacks on civilians are a grave matter.” He said that since “North Korea maintains an offensive posture,” South Korea’s military forces — the army, air force and navy — “should unite and retaliate against [the North’s] provocation with multiple-fold firepower.”

“Reckless attacks on South Korean civilians are not tolerable, especially when South Korea is providing North Korea with humanitarian aid,” Lee said, according to Yonhap.

“As for such attacks on civilians, a response beyond the rule of engagement is necessary. Our military should show this through action rather than an administrative response” such as statements or talks, he said.

After the incident, Yonhap said the Seoul government “banned its nationals from entering the communist state, indefinitely postponed their scheduled Red Cross talks and began looking at ways to push the United Nations to condemn Pyongyang.”

This latest action occurred during South Korean maritime military drills. North Korea said the incident stemmed from those exercises, code named Hoguk, and called the activity “war maneuvers for a war of aggression.”

The “South Korean puppet group” engaged in “reckless military provocation” by firing “dozens of shells” inside its territorial waters “despite the repeated warnings of the DPRK” or Democratic People’s Republic of Korea, the North’s military said in a statement.

“The revolutionary armed forces of the DPRK standing guard over the inviolable territorial waters of the country took such a decisive military step as reacting to the military provocation of the puppet group with a prompt powerful physical strike,” the statement said.

“It is a traditional mode of counter-action of the army of the DPRK to counter the firing of the provocateurs with merciless strikes,” said the statement, which warned that it “will unhesitatingly continue taking merciless military counter-actions against it” if the border is crossed.

A senior U.S. defense official said South Korea informed North Korea before firing its first artillery rounds, as part of that training mission, and that “there’s no reason North Korea should have been surprised by this firing of artillery.”

The U.S. military does not publicly announce its military posture or “state of readiness,” but no changes have been observed from what U.S. forces in Korea were doing before this attack. The official says that North Korea has a history of unpredictable behavior and that “in some ways, this is not surprising for them.”

Some U.S. forces had been helping the South Koreans in their training exercises, but were not in the shelled area.

Stephen Bosworth, the U.S. special envoy on North Korean denuclearization, urged restraint on both sides when he spoke to reporters about the incident. He was in Beijing to discuss nuclear matters with Chinese diplomats.

“The U.S. strongly condemns this aggression on the part of North Korea, and we stand firmly with our allies. The subject did, of course, come up in my meetings with the Chinese Ministry of Foreign Affairs. I think we both share the view that such conflict is very undesirable. I expressed to them the desire that restraint to be exercised on all sides, and I think we agree on that.”

This incident comes after a U.S. scientist reported that North Korea has a new uranium enrichment facility. North Korean officials said the facility is operating and producing low-enriched uranium, according to Stanford University professor Siegfried Hecker.

The enrichment facility contains 2,000 centrifuges and appears to be designed for nuclear power production, “not to boost North Korea’s military capability,” Hecker says.

But U.S. and South Korean diplomats said the latest revelation confirms the country’s long-term deceit.

Sanctions have been progressively placed on North Korea in response to a succession of nuclear and missile tests and the sinking of the South Korean warship in March.

The United States said it would not dismiss restarting six-party talks aimed at denuclearizing the North. However, it said it would not return to negotiations unless North Korea showed good faith.

Countries that had been negotiating with North Korea over its nuclear program issued swift reactions. The six-party talks include both Koreas, the United States, Russia, Japan and China.

The United States “strongly” condemned North Korea’s action, and a U.S. Defense Department official said that the “hope is that this is just one isolated incident, not an escalation into a different military posture” by the North.

U.S. President Barack Obama, who said he deplored the action and plans to call President Lee, said he doesn’t believe North Korea is living up to its obligations. U.S. Rep. John Boehner, the House Republican leader who’s in line to become the next speaker, said he joined Obama in condemning North Korea’s “hostile action.”

Chinese Foreign Ministry spokesman Hong Lei said China had “taken note of relevant reports” and expressed its “concern.” “Relevant facts need to be verified, and we hope both parties make more contributions to the stability of the peninsula,” he said.

Russia’s Interfax news agency said Russia condemned North Korea’s artillery shelling and said “those who initiated the attack on a South Korean island in the northern part of the inter-Korean maritime border line assumed enormous responsibility.”

Japanese Prime Minister Naoto Kan’s cabinet held a ministerial meeting, and Chief Cabinet Secretary Yoshito Sengoku announced a government statement condemning North Korea and calling the act “unpardonable.”

Asked whether the violence in the Yellow Sea would make resumption of six-party talks more difficult, Bosworth said, the “resumption of the six-party talks has never been an easy process.” A formal round of talks was last held a few years ago.

“We strongly believe that a multilateral diplomatic approach is the only way to realistically to resolve these problems.”

U.N. Secretary-General Ban Ki-moon urged that “any differences should be resolved by peaceful means and dialogue.”

A U.S. official with knowledge of U.S. strategy on North Korea says it may be time to adjust U.S. military policy in the region.

While the exercises “are designed to deter further provocative behavior by North Korea, obviously it’s not working. When we announced joint military exercises in the Yellow Sea, it only angered China. And in other waters, it doesn’t seem to be effective deterrence against the North Koreans,” the official said.

Coming on the heels of the Cheonan sinking, the Asia Foundation’s Snyder said the act “raises fundamental questions regarding what sorts of internal stresses the regime may be facing.”

“It also signals dissatisfaction with the inter-Korean relationship and an apparent willingness to keep inter-Korean tensions high. The incident could reflect a more aggressive view of what a nuclear North Korea thinks it can do without facing a broader escalation of tensions.”

— Journalist Andrew Salmon and CNN’s Steven Jiang, Yoko Wakatsuki and Joe Sterling contributed to this report.