South Korea's new president on Monday promised a strong military response to any North Korean provocation after Pyongyang announced that the two countries were now in a state of war.

President Park Geun-Hye's warning came as North Korea's rubber-stamp parliament formalised the country's status as a nuclear weapons state and appointed a sacked economic reformer for a fresh term as prime minister.

It also coincided with a US announcement that it had deployed stealth fighters to South Korea as part of an ongoing joint military exercise.

At a meeting with senior military officials and Defence Minister Kim Kwan-Jin, Park said she took the near-daily stream of bellicose threats emanating from the North over the past month "very seriously".

"I believe that we should make a strong and immediate retaliation without any other political considerations if (the North) stages any provocation against our people," she said.

Her defence minister made it clear that the South would carry out pre-emptive strikes against the North's nuclear and missile facilities in the event of hostilities breaking out.

"We will... establish a so-called 'active deterrence' aimed at neutralising the North's nuclear and missile threats quickly," Kim said.

The Korean peninsula has been caught in a cycle of escalating tensions since the North's long-range rocket launch in December which its critics condemned as a ballistic missile test.

United Nations sanctions were followed by a nuclear test in February, after which came more sanctions and apocalyptic threats from Pyongyang as South Korea and the United States conducted joint military drills.

Those threats have run the gamut from warnings of limited artillery bombardments to pre-emptive nuclear strikes, and have been met with counter-warnings from Seoul and Washington of severe repercussions.

The White House said Monday that despite the North's threats, North Korea had yet to back up its words with mass troop mobilizations or troop movements.

"Despite the harsh rhetoric we're hearing from Pyongyang, we are not seeing changes to the North Korean military posture, such as large-scale mobilizations and positioning of forces," White House spokesman Jay Carney said.

The US military said Monday it had deployed F-22 Raptor stealth fighters to South Korea as part of the ongoing "Foal Eagle" military exercise.

"The F-22s are advanced fighter aircraft and they're an important display of our commitment to the South Korean alliance," Pentagon spokesman George Little told reporters in Washington.

"The North Koreans have a choice. They can continue to engage in provocations, with bellicose, overheated, irresponsible rhetoric, or they can choose the path of peace," he said.

North Korea has already threatened to strike the US mainland and US bases in the Pacific in response to the participation of nuclear-capable US B-52 and B-2 stealth bombers in the exercise.

Monday's gathering of the North's Supreme People's Assembly, or parliament, was notable for the promotion of a former premier who was sacked in a reported backlash against his pursuit of economic reforms.

Pak Pong-Ju, 74, was unanimously returned to the post of prime minister which he had previously held from 2003-2007, when he spearheaded modest economic reforms of state enterprises.

An apparent backlash from the party and the military saw him suspended from duty in June 2006 and sacked the following year.

The parliament also adopted an ordinance on "consolidating the position of nuclear weapons state for self-defence", KCNA said, fulfilling the party leadership's call a day before for the country's possession of nuclear weapons to be "fixed by law."

Sunday's gathering of the central committee of the ruling Workers' Party, which was chaired by leader Kim Jong-Un, had also insisted that the nuclear arsenal be beefed up "qualitatively and quantitatively".

On Saturday the North announced it had entered a "state of war" with South Korea and warned that any provocation would swiftly escalate into an all-out nuclear conflict.

It also threatened to shut down the joint-Korean Kaesong industrial complex, which is a crucial source of hard-currency revenue for Pyongyang and has been shielded from previous crises.

The border crossing to Kaesong, which lies 10 kilometres (six miles) inside the North, was functioning normally on Monday.

The operating stability of the complex is seen as a bellwether of inter-Korean relations, and its closure would mark a clear escalation of tensions beyond all the military rhetoric.