SEOUL, South Korea — North Korea threatened “immediate counteractions” if shells fired as part of military drills hit its waters, as the United States and South Korea conducted annual anti- submarine exercises in the region.

U.S. and South Korean forces are trying “to push the present state of war to an actual war,” the official Korean Central News Agency said Tuesday. The two allies on April 30 concluded the annual two-month Foal Eagle exercises, which rehearse ground-based operations.

The warning from Kim Jong Un’s regime coincides with a trip by South Korean President Park Geun Hye to Washington. Park will meet President Barack Obama to discuss ways to end a standoff with the North that intensified after Kim defied U.N. sanctions with a nuclear weapon test in February.

The North has warned of atomic strikes against the United States and South Korea, sentenced a U.S. citizen to 15 years of hard labor and shuttered a factory park run jointly with the South.

“It’s premature to make a judgment about whether the North Korean provocation cycle is going up, down or zig-zagging,” Daniel Russel, senior director for Asian affairs at the White House National Security Council, told reporters yesterday in Washington. “It will take some time to play out.”

A “grand fireworks display” by North Korea can’t be ruled out, Russel said. He declined to comment on a CNN report that said the North moved two ballistic missiles away from its eastern coast.

The U.S. and South Korean navies are conducting drills focused on anti-submarine warfare training, U.S. Seventh Fleet spokesman Ron Steiner said in an email Tuesday. He declined to confirm a North Korean claim that the nuclear-powered USS Nimitz aircraft carrier would participate in another round of drills starting around May 10.

Strengthen Alliance

The Nimitz is in the region and the United States routinely seeks opportunities to train with South Korea to ‘strengthen the alliance,’’ Steiner said. South Korean Defense Ministry spokesman Kim Min Seok also declined to confirm reports that the Nimitz would dock in Busan.

North Korean military units stationed on the southwestern front will respond immediately if a “single shell” drops in its waters from the U.S. and South Korean drills, KCNA said.

“‘In case the enemies recklessly counter our counter- strikes, all striking forces will turn the five islands in the West Sea of Korea into a sea in flames,’’ it said.

Park left Seoul for the United States on May 5 for her first overseas trip since taking office in February. Park and Obama will discuss boosting cooperation after the North last month refused calls to restart nuclear disarmament talks.

South Korea will issue military response against any future North Korean provocation to ‘‘make them pay,’’ Park said in an interview with CBS Monday.

‘‘North Korea engages in provocations, threats,’’ she said. ‘‘This is followed by negotiations and assistance, and so we saw an endless continuation of this vicious cycle, and it is time for us to put an end to the cycle.’’