SEOUL, South Korea — The United States military said Monday that it had signed an agreement with South Korea on how to counter provocations from North Korea.

The deal, struck on Friday, defines the role that United States forces would play in dealing with what South Korean military officials called local clashes and skirmishes, like the shelling of an island near the border in 2010 by the North, which killed four South Koreans.

The two allies described the new contingency plans developed after that episode as “South Korean-led, U.S.-supported.” They lay out various types of provocations and a joint South Korean-American response for each type, South Korean officials said. Putting those commitments down on paper will help deter provocations, they said.

The two allies refused to disclose specifics about how far the United States would go in its supporting role, especially at what point American troops would directly join a South Korean counterattack against a North Korean provocation.