North Korea on Tuesday threatened the South with "sledge-hammer" military action over anti-Pyongyang protests in Seoul and rejected the idea of entering into a "humiliating" dialogue with the United States.

Both statements came a day after US Secretary of State John Kerry wrapped up a Northeast Asian tour aimed at defusing soaring military tensions on the Korean peninsula and getting China to help rein in a belligerent Pyongyang.

US President Barack Obama predicted new provocations from North Korea in a television interview aired later on Tuesday but said that he did not believe North Korea could yet arm a missile with a nuclear warhead.

The president was asked in the interview with NBC's Today Show whether Pyongyang currently had the capability to arm a ballistic missile with a nuclear bomb.

"Based on our current intelligence assessments we do not think they have that capacity," Obama said in the interview recorded on Monday.

"But we have to make sure that we are dealing with every contingency out there and that's why I've repositioned missile defense systems to guard against any miscalculation on their part."

Pyongyang's latest threat against the South followed a demonstration by conservative activists in Seoul who burned effigies of North Korea's late founder Kim Il-Sung, his son Kim Jong-Il and grandson and current leader Kim Jong-Un.

The protest coincided with North Korean celebrations Monday of Kim Il-Sung's birthday -- one of the most important dates in the national calendar.

Condemning what it described as a "thrice-cursed... monstrous criminal act", the Korean People's Army (KPA) Supreme Command issued an "ultimatum" threatening immediate action if no apology was forthcoming.

"Our retaliatory action will start without any notice," it said in a statement.

"The military demonstration... will be powerful sledge-hammer blows at all hostile forces hurting the dignity of the supreme leadership," it added.

Intelligence reports suggest the North has had two medium-range missiles primed to fire from its east coast for at least a week, with most observers predicting a launch sometime around the date of Kim Il-Sung's birthday.

South Korea's defence ministry called Tuesday's ultimatum "regrettable" and promised to retaliate "thoroughly and resolutely" to any provocation.

The Korean peninsula has been in a state of heightened military tension since the North carried out its third nuclear test in February.

Incensed by fresh UN sanctions and joint South Korea-US military exercises, Pyongyang has spent weeks issuing blistering threats of missile strikes and nuclear war.

During his whirlwind tour of South Korea, China and Japan, Kerry had raised the prospect of "authentic" negotiations if Pyongyang took "meaningful steps" to show it would honour past commitments.

Kerry did not specify what form any negotiations might take. In the past Washington has refused direct talks with Pyongyang, insisting instead on using the forum of the six-party talks on North Korea.

North Korea has always desired direct talks, but on Tuesday its foreign ministry rejected the prospect of negotiations, saying Washington would first have to abandon its "hostile" policies.

"We do not oppose dialogue, but cannot sit face-to-face at the humiliating dialogue table with the other party who is wielding a nuclear stick," a ministry spokesman said in a statement issued on state media.

North Korea has regularly accused the US of preparing to launch a nuclear strike on its territory, and reacted furiously to the use of nuclear-capable B-52s and B-2 stealth bombers in the joint South-US military drills.

The missiles mobilised by the North for a possible launch are reported to be untested Musudan models with an estimated range of up to 4,000 kilometres (2,485 miles).

That would cover any target in South Korea and Japan, and possibly even US military bases on the Pacific island of Guam.