SEOUL, South Korea  A North Korean ship shadowed by an American Navy destroyer and possibly heading toward Myanmar on Sunday could pose the first test of how far the United States and its allies will go under a new United Nations resolution to stop the North’s military shipments.

The United States began tracking the ship, the 2,000-ton freighter Kang Nam, after it left Nampo, a port near Pyongyang, the North’s capital, on Wednesday.

Pentagon officials have said they suspect the ship is carrying prohibited materials, but they have declined to say where it may be headed. A South Korean cable news network, YTN, on Sunday quoted an unidentified intelligence source as saying that Myanmar was the destination of the freighter, which may be carrying missile components.

North Korea has said it would consider interception an “act of war” and react accordingly.

Over the weekend, the North’s state-run news media said the country vowed to “respond to sanctions with retaliation” and threatened “unlimited retaliatory strikes” against South Korea if it cooperated with the sanctions imposed by the United Nations Security Council.