North Korea hasn't responded to U.S. attempts to discuss the American soldier who bolted across the heavily armed border, officials in Washington said Thursday, underscoring that the serviceman's prospects for a quick release are unclear at a time of high tensions and inactive communication channels.

Without mentioning the soldier, North Korea's defense minister instead issued a veiled threat Thursday, suggesting that the docking of a nuclear-armed U.S. submarine in South Korea could be grounds for a nuclear attack by the North. North Korea has used such rhetoric before, but the latest threat could signal just how strained ties are right now.

Pvt. Travis King, who was supposed to be on his way to Fort Bliss, Texas, after finishing a prison sentence in South Korea for assault, ran into North Korea while on a civilian tour of the border village of Panmunjom on Tuesday. He is the first known American held in North Korea in nearly five years.

According to a U.S. official, King — who chose to serve his time at a labor camp rather than pay the nearly $4,000 fine — has been declared AWOL. The punishment for being away without leave can include confinement in the brig, forfeiture of pay or dishonorable discharge and it is largely based on how long they were away and whether they were apprehended or returned on their own. The official spoke on condition of anonymity to discuss a sensitive matter.

King, 23, has not been declared a deserter, which is a far more serious offense. Often the military waits for a period of time to see if a service member returns, but that is very uncertain in this case. Desertion can result in imprisonment of as much as three years, and — in times of war — can carry the death penalty.

Matthew Miller, a spokesperson for the U.S. State Department, told reporters Thursday in Washington there has been no response from the North Koreans.

"The White House, the State Department, the Pentagon of course are all continuing to work together on this matter to ascertain information about the well-being and whereabouts of Private King" Miller said. "We have relayed messages to the DPRK that Private King crossed on his own and we want him returned safely. We have also asked for more info on his well-being."

The U.S. and North Korea, which fought during the 1950-53 Korean War, are still technically at war since that conflict ended in a truce, not a peace treaty, and have no diplomatic ties. Sweden provided consular services for Americans in past cases, but Swedish diplomatic staff reportedly haven't returned since North Korea ordered foreigners to leave the country at the start of the COVID-19 pandemic.

The U.S. can also reach North Korea via a hotline at the U.S.-led U.N. Command in Panmunjom — known as the " pink phone."

Miller said Wednesday the State Department has reached out to officials in South Korea and Sweden. Jeon Ha-kyu, a spokesperson of South Korea's Defense Ministry, said Thursday his ministry is sharing information with the American-led U.N. Command in South Korea, without elaborating.

Meanwhile, the North's defense minister, Kang Sun Nam, issued a statement in state media that called a recent U.S. submarine deployment "the most undisguised and direct nuclear threat" to North Korea. He warned the deployment may be one of the situations foreseen in a new law that authorized the preemptive use of nuclear weapons in a broad range of cases.

"The U.S. military side should realize that its nuclear assets have entered extremely dangerous waters," Kang said.

Some experts still doubt North Korea could use such arms first in the face of superior U.S. and South Korean forces.

The deployment, which happened on the day of King's border crossing, was part of U.S. steps to boost its security commitment to the North's rival, South Korea. North Korea later test-fired two missiles.

The tensions could complicate efforts to free King.

"North Korea is not going to 'catch and release' a border-crosser. ... However, the Kim regime has little incentive to hold an American citizen very long, as doing so can entail liabilities," said Leif-Eric Easley, a professor at Ewha University in Seoul.

"For Pyongyang, it makes sense to find a way of extracting some compensation and then expel an American for unauthorized entry into the country before an isolated incident escalates in ways that risk North Korean diplomatic and financial interests," he said.

Other experts say North Korea won't likely easily return King as he is a soldier who apparently voluntarily fled to North Korea, though many previous American civilian detainees were released after the United States sent high-profile missions to Pyongyang to secure their freedom.

North Korea has previously held a number of Americans who were arrested for anti-state, espionage and other charges. But no other Americans were known to be detained since North Korea expelled American Bruce Byron Lowrance in 2018. During the Cold War, a small number of U.S. soldiers who fled to North Korea later appeared in North Korean propaganda films.

The motive for King's border crossing is unknown. King's family members said the soldier may have felt overwhelmed by legal trouble in South Korea that could lead to a discharge from the military.

King, who was serving in South Korea as a cavalry scout with the 1st Armored Division, was released earlier this month after 47 days of hard labor in the prison camp. In February, a Seoul court fined him 5 million won ($3,950) after convicting him of assaulting someone and damaging a police vehicle, according to a transcript of the verdict obtained by The Associated Press. The ruling said King had also been accused of punching a man at a Seoul nightclub, though the court dismissed that charge because the victim didn't want King to be punished.