United Nations, United States: "The detention of the Mu Du Bong is a rampant violation of the dignified sovereignty of the DPRK," he said, referring to the Democratic People's Republic of Korea.
"We will take necessary measures to make the ship leave immediately", he said.
The Security Council blacklisted the Ocean Maritime Management company in July over an attempt to ship arms to North Korea from Cuba.
The North Korean diplomat said a crew of 50 North Koreans were being held with the ship and added: "Their families are crying for their return."
Ricardo Alday, spokesman for Mexico's UN mission, said there were 33 North Korean nationals in Tuxpan and that talks were under way with Pyongyang to allow them to return home.
"This is not an illegal action," Alday told AFP. "We are fulfilling our international obligation under Security Council resolutions."
The Security Council already has a series of sanctions in force against North Korea over its nuclear program and missile launches.
A report by a UN panel of expert in February found that Pyongyang was still trying to purchase items to bolster its nuclear and missile programs.
The 6,500-tonne Mu Du Bong hit a coral reef in the Gulf of Mexico on July 14, apparently due to a navigational error, Mexican officials said.
The North Korean envoy said Pyongyang had compensated Mexico for the environmental damage to the reef.
An Myong Hun accused the United States of pressuring Mexico to refuse to release the ship.
North Korea accused Mexico on Wednesday of illegally detaining a ship and denied that it was linked to a firm blacklisted under UN sanctions.
The Mu Du Bong ran aground near the port of Tuxpan in July and was later impounded over its ties to North Korea's Ocean Maritime Management firm, which has been targeted by UN sanctions.
"The Mu Du Bong is a peaceful merchant ship," North Korea's deputy representative An Myong Hun told reporters at the North Korean mission.
"We will take necessary measures to make the ship leave immediately", he said.
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The North Korean diplomat said a crew of 50 North Koreans were being held with the ship and added: "Their families are crying for their return."
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"This is not an illegal action," Alday told AFP. "We are fulfilling our international obligation under Security Council resolutions."
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A report by a UN panel of expert in February found that Pyongyang was still trying to purchase items to bolster its nuclear and missile programs.
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The North Korean envoy said Pyongyang had compensated Mexico for the environmental damage to the reef.
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