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(CNN) -- North Korea has upped the temperature on its neighbors, warning in a new threat that it would not give any advance notice before attacking South Korea.
"Our retaliatory action will start without any notice from now," Pyongyang said in a statement published Tuesday by its official news agency, KCNA.
North Korea said it was responding to what it called insults from the "puppet authorities" in the South, claiming that there had been a rally against North Korea in Seoul.
It called the rally a "monstrous criminal act."
The renewed threats came a day after North Koreans celebrated the birthday of their country's founder, Kim Il Sung, who launched the Korean War.
On Monday, U.S. Secretary of State John Kerry urged the regime in Pyongyang to ditch its nuclear program and put a lid on its fiery rhetoric if it wants to hold talks.
"The United States has made clear many times what the conditions are for our entering talks and they haven't changed," Kerry said during an interview with CNN's Jill Dougherty in Tokyo.
"The conditions have to be met where the North has to move towards denuclearization, indicate a seriousness in doing so by reducing these threats, stop the testing, and indicate it's actually prepared to negotiate," he said.
Kerry was speaking at the end of a three-day trip that focused on securing fresh commitments from South Korea, China and Japan to try to persuade Pyongyang to return to the negotiating table and renounce nuclear weapons.
His visit followed weeks of dramatic threats by Kim Jong Un's regime, including that of a nuclear strike on the United States and South Korea.
The White House announced Monday that South Korean President Park Geun-hye will visit President Barack Obama in Washington on May 7.
"President Park's visit underscores the importance of the U.S.-ROK (Republic of Korea) alliance as a linchpin of peace and security on the Korean Peninsula and in the Asia Pacific region, and of the central role of alliances in the President's Asia-Pacific rebalancing effort," the White House said in a statement.
There is uncertainty about how advanced the North's nuclear weapons program is, but Kerry on Monday reiterated the U.S. government view that Pyongyang doesn't yet have the capacity to carry out a nuclear attack.
Last month, North Korea scrapped the 1953 truce that effectively ended the Korean War and said it was nullifying the joint declaration on the denuclearization of the Korean Peninsula.
It also recently pledged to restart a reactor at its main nuclear complex that had been shut down under an agreement reached in October 2007 during talks with the United States, South Korea and four other countries.
Kerry said Monday that the United States is concerned that North Korea's dogged pursuit of its nuclear weapons program could have consequences elsewhere in the world.
"It is the belief of President Obama, myself and the administration that what happens here also has an impact on perceptions in places like Iran, the Middle East, and elsewhere where we're engaged in nonproliferation efforts," he said.
Pyongyang insists that its nuclear weapons are a necessary deterrent because of the threat posed to it by the United States and its allies.
Multilateral talks on North Korea's nuclear program have ended in failure in the past, and Kerry said the United States isn't interested in going over old ground.
"We're not going to go through another cycle of artificial negotiations that are geared to simply attract some kind of aid or lull in events while they continue to pursue their devices' designs," he said.
A U.S. State Department official said Monday there are no plans to move toward direct talks, "because North Korea has shown no willingness to move in a positive direction."
Pyongyang on Sunday rejected a different proposal for dialogue, one by South Korea last week regarding the North's suspension of activity at the manufacturing zone that the two countries jointly operate.
A statement via KCNA, the state-run news agency, called the South's offer a "crafty trick" and "empty words without any content."
And a KCNA commentary Monday was titled, "U.S. is to blame for escalating tension on Korean Peninsula."
Kerry's trip finishes on one of the biggest dates on the North Korean calendar: "The Day of the Sun," when citizens celebrate the birthday of Kim Il Sung, remembered as the "eternal president." He died in 1994 and would have been 101 this year.
Current leader Kim Jong Un paid tribute Monday to Kim Il Sung, his grandfather, as well as his late father, Kim Jong Il, by visiting the halls where both men lie in state. It was believed to be the young leader's first public appearance in two weeks.
Suspicions remain that the North could carry out a test of a mobile ballistic missile at any time.
Kerry said in Beijing at the weekend that the United States and China are calling on North Korea to refrain from any provocative steps -- including any missile launches.
Pyongyang made good on its promise to launch a long-range rocket around the time of Kim Il Sung's birthday last year; the rocket broke apart after launch and fell into the sea.
North Korea has made more threats since then. It launched a rocket in December that apparently put a satellite into orbit, and in response, the U.N. Security Council approved broadening sanctions against the country.
Angered by those sanctions, Pyongyang announced in January it was planning its third nuclear test and more long-range rocket launches as part what it called a new phase of confrontation with the United States.
It carried out an underground nuclear bomb test in February, resulting in even tougher sanctions. Those measures, along with joint U.S.-South Korean military exercises in South Korea, prompted an intensification in the North's threats.
CNN's Richard Allen Greene, Esprit Smith, Elizabeth Joseph and Tim Schwarz contributed to this report.