INCHEON, South Korea — Rescuers found the burned bodies today of two islanders killed in a North Korean artillery attack — the first civilian deaths from a skirmish that marked a dramatic escalation of tensions between the rival Koreas.

The barrage on the tiny island of Yeonpyeong in the western waters near the Koreas’ maritime border also killed two South Korean marines and wounded 18 others Tuesday in what U.N. Secretary-General Ban Ki-moon called one of the “gravest incidents“ since the Korean War.

As South Korean troops remained on high alert and buildings continued to burn, exhausted evacuees streamed into the port city of Incheon after spending the night in underground shelters, embracing tearful family members and telling harrowing tales of destruction.

President Barack Obama underlined Washington’s pledge to “stand shoulder to shoulder” with Seoul, and called upon China to restrain ally Pyongyang. Seoul and Washington reaffirmed plans to stage joint military exercises later this week in the Yellow Sea, just 70 miles south of the island.

The U.S. stations more than 28,000 troops in South Korea to guard against North Korean aggression, a legacy of the bitter three-year conflict that ended in a truce, not a peace treaty, in 1953.

In Pyongyang, residents boasted that the exchange showed off their military’s strength and ability to counter South Korean aggression.

“I think this time our military demonstrated to the whole world that it doesn’t make empty talk,” Ri Pong Suk told TV news agency APTN in North Korea.

Artillery and gunfire break out sporadically along the land and maritime borders dividing the two Koreas, and have erupted into deadly exchanges four times since 1999.