Pyongyang also said it intends to try detained Americans in its custody under "wartime law," South Korean news agency Yonhap reported.
"If our request to immediately withdraw sanctions is not accepted by [the United States], we will carry out, step-by-step, corresponding practical measures," the statement on state-controlled KCNA read. "The first step is to completely block the New York channel of communication that uniquely exists between North Korea and the United States."
The statement was delivered to the U.S. government from the Permanent Mission of North Korea to the United Nations on Sunday, according to KCNA.
On Friday North Korea had issued a separate statement from its foreign ministry, vowing to apply wartime law to "all issues related to the United States."
"The issue of detained Americans is no exception," the statement read.
Chang Yong-seok, a senior researcher at the Institute for Peace and Unification Studies at Seoul National University, said the statements taken together mean Pyongyang has no plans to resolve the issue of U.S. detainees through diplomatic channels.
In March North Korea sentenced University of Virginia student Otto Warmbier to 15 years of hard labor after detaining him in January.
In April U.S. citizen Kim Dong Chul was sentenced to 10 years in prison with hard labor after being charged of spying and transporting state secrets on a flash drive.
"The accused, Kim Dong Chul, schemed to take down the highest dignity and political system of [North Korea]," KCNA had stated during the trial.