The 2,000-ton freighter Kang Nam left North Korea last Wednesday and is reportedly on its way to Myanmar.
Pentagon officials say they suspect the ship is carrying prohibited materials.
The Kang Nam
is the first North Korean vessel to be tracked under a new UN Security council resolution passed in response to the nuclear test carried out by the North last month.
The sanctions firm up an earlier arms embargo and authorise ship searches in an attempt to thwart North Korea's nuclear and ballistic missile programmes.
North Korea has said it would view any such searches as an act of war.
With tensions high, Barack Obama, the US president, has said he is ready to cope with "any contingencies" involving North Korea amid reports that North Korea may be preparing for another long range missile test.
Japanese media reports have said the test may be timed to coincide with US independence day on July 4.
Speaking to the US TV network CBS, Obama said the US was prepared for any North Korean provocation, including the possibility of a North Korean missile test toward Hawaii.
Robert Gates, the US defence secretary, has ordered additional protections for Hawaii as a precaution.
"This administration - and our military - is fully prepared for any contingencies," Obama told CBS, in an interview due to be broadcast on Monday.
"I don't want to speculate on hypotheticals," Obama said. "But I want… to give assurances to the American people that the t's are crossed and the i's are dotted in terms of what might happen."