President Obama, meanwhile, has told CBS News the U.S. is ready to cope with "any contingencies" involving North Korea and vowed not to "reward belligerence and provocation."
South Korea's YTN news network reported Sunday that a suspected of carrying missiles and related parts was headed toward Myanmar in what could be the first test of new U.N. sanctions against the North over its recent nuclear test.
Tune in to The Early Show Monday morning at 7 a.m. EDT on CBS to see Harry Smith discuss the North Korea standoff with President Obama. To watch Part 1 of the interview, aired on Sunday, in which Mr. Obama discusses fatherhood, click here.
The sanctions - punishment for an underground nuclear test North Korea conducted May 25 - firm up an earlier arms embargo against North Korea and authorize ship searches in an attempt to thwart the regime's nuclear and ballistic missile ambitions.
On Monday, North Korea's main Rodong Sinmun newspaper called it "nonsense" to say the country is a threat to the U.S., and instead claimed Washington was the one threatening the North. The paper also warned in a commentary that the country is prepared to strike back if attacked.
"As long as our country has become a proud nuclear power, the U.S. should take a correct look at whom it is dealing with," the editorial said. "It would be a grave mistake for the U.S. to think it can remain unhurt if it ignites the fuse of war on the Korean peninsula."
The Rodong Sinmun also denounced Mr. Obama's recent pledge to defend and protect South Korea - even promising to keep Seoul "under the U.S. nuclear umbrella" - as an attempt to attack the North with atomic bombs. Mr. Obama made the commitment in a joint statement after aLee Myung-bak.
North Korea calls its nuclear program a deterrent against the U.S., which Pyongyang routinely accuses of plotting to topple the communist regime. The U.S., which has 28,500 troops in South Korea, has said it has no such intentions, and has no nuclear weapons on the Korean peninsula.
Mr. Obama said the U.S. is prepared for any North Korean provocation, including the regime's reported threat to.
Japanese media have reported that the North Koreans appear to be preparing for a long-range test planned sometime around July 4, the Independence Day holiday. Defense Secretary Robert Gates has ordered additional protections for Hawaii as a precaution.
"This administration - and our military - is fully prepared for any contingencies," Mr. Obama told CBS Early Show co-anchor Harry Smith.
"I don't want to speculate on hypotheticals," Mr. Obama told Smith. "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."
A North Korean cargo ship, the Kang Nam, is expected to travel to Myanmar via Singapore, YTN said, citing an unidentified intelligence source in South Korea.
Myanmar's military government, which faces an arms embargo from the United States and the European Union, reportedly has bought weapons from the North in the past.
Two U.S. officials said Thursday that the U.S. military had begun tracking the ship, which left a North Korean port on Wednesday.
One official said it was uncertain what the Kang Nam was carrying but that it had been involved in weapons proliferation before. Both spoke on condition of anonymity in order to discuss intelligence.
A senior U.S. military official told The Associated Press on Friday that a Navy ship, the USS John S. McCain, is relatively close to the North Korean vessel but had no orders to intercept it under the Security Council resolution and had not requested that authority. The official spoke on condition of anonymity because of the sensitivity of the issue.
The U.S. ship, a guided missile destroyer, is named after the grandfather and father of former U.S. presidential candidate Sen. John McCain. Both were admirals.
McCain said Sunday that the U.S. should board the Kang Nam even without North Korean permission if hard evidence shows it is carrying missiles or other cargo in violation of U.N. resolutions.
"I think we should board it. It's going to contribute to the proliferation of weapons of mass destruction to rogue nations that pose a direct threat to the United States," he said on CBS' "Face the Nation."