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North Korea is continuing its threats against the United States, saying Monday it will end a diplomatic communication channel with the United States.

According to The Associated Press, Pyongyang hinted at harsher punishment for Americans detained in the country in retaliation for U.S. sanctions that target leader Kim Jong Un.

The U.S. government last week imposed penalties on Kim and 10 other top officials for alleged human rights abuses. North Korea is already sanctioned because of its nuclear weapons program, but last week's move was the first time that Kim has been personally sanctioned.

The North called the sanctions tantamount to a war declaration and threatened a tough response.

On Monday, the North's state media said it told the United States it will terminate contact through a UN channel in New York that allowed diplomats to communicate, according to AP.

The New York channel refers to a method for North Korea's U.N. diplomats to communicate with U.S. diplomats in New York. This is needed because the countries don't have diplomatic ties and their animosities have deepened because of the North's nuclear and missile programs.

Monday's threat came a day after Pyongyang threatened a "physical response" to a move by the United States and South Korea to deploy the advanced THAAD missile defense system to the Korean peninsula.

In Washington on Monday, State Department spokesman John Kirby did not directly address the fate of the New York channel. In comments to reporters, he called on North Korea "to refrain from actions and rhetoric that only further raise tensions in the region."

He added he would not comment on the details of diplomatic exchanges, according to AP.

The North's actions could complicate U.S. efforts to secure the release of at least two American citizens being held for alleged espionage, subversion and other anti-state activities. One is serving a 10-year prison term with hard labor while the other received 15 years.

Kirby urged North Korea to adhere to the Vienna Convention on Consular Relations and grant consular access to any detained U.S. citizens without delay. He also reiterated a call for the Americans to be freed.

The North frequently threatens to attack the South and U.S. interests in Asia and the Pacific. In fact, Kim several weeks ago boasted that his country possesses "the sure capability to attack" U.S. interests in the Pacific.