Story highlights North Korea says it would not give notice before attacking South Korea

John Kerry says North Korea needs to show its serious about denuclearization

He says the North's actions can affect the situation in Iran and other countries

Kerry spoke at the end of a three-day trip focused on the Korean situation

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.

Photos: Photos: Militaries and Korean tensions Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – Emergency service personnel wearing chemical protective clothing participate in an anti-chemical warfare exercise on Tuesday, April 16 in Seoul. Tensions remain high in the Korean Peninsula in the wake of North Korea's recent nuclear threats and provocations. A Pentagon intelligence assessment suggests the North may have the ability to deliver a nuclear weapon with a ballistic missile, though the reliability is believed to be "low." Hide Caption 1 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean marines arrive on the island of Yeonpyeong near the disputed waters of the Yellow Sea on Friday, April 12. Hide Caption 2 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – A Japanese soldier is on alert as Patriot Advanced Capability-3 missile launchers are deployed at the Defense Ministry in Tokyo on Wednesday, April 10. Hide Caption 3 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers sit in a truck at the Inter-Korean transit office on Tuesday, April 9, in Paju, South Korea. Hide Caption 4 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers participate in an artillery drill as part of the Foal Eagle joint military exercise by U.S. and South Korean forces near the Demilitarized Zone in Goseong on April 9. Hide Caption 5 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – U.S. soldiers are at a military training field in Yeoncheon, South Korea, on April 9. Hide Caption 6 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers with K-55 self-propelled Howitzers stage at a military training field in the border city of Paju on Friday, April 5, as tensions continue to mount on the Korean peninsula. Hide Caption 7 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers man a cannon at a military training field in Paju on April 5. Hide Caption 8 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers stand guard at a sentry post at the border with North Korea in the Demilitarized Zone near Imjingak, South Korea, on April 5. Hide Caption 9 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – A U.S. Army Patriot missile battery is visible at the U.S. Osan Air Base in South Korea on Friday, April 5. Hide Caption 10 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – The U.S. Navy is moving a sea-based radar platform, like the one seen in this 2006 file photo, closer to the North Korean coast to monitor that country's military moves, including possible new missile launches, a Defense Department official said Monday, April 1. Hide Caption 11 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean marines man K-55 self-propelled Howitzers at a military training field in the border city of Paju on Monday, April 1. Park Geun-hye, South Korea's new president, promised a strong military response to any North Korean provocation after North Korea announced that the two countries were in a state of war. Hide Caption 12 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean anti-aircraft armored vehicles move across a temporary bridge during a river crossing drill in Hwacheon near the North Korean border on Monday, April 1. Hide Caption 13 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers ride on a military truck in Paju on Friday, March 29. Hide Caption 14 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – The United States said Thursday, March 28, that it flew stealth bombers over South Korea to participate in annual military exercises amid spiking tensions with North Korea. Pictured, a B-2 Spirit stealth bomber flies over South Korea's western port city of Pyeongtaek. Hide Caption 15 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers gather at the foot of a mountain near a military drill field in the border city of Paju on Wednesday, March 27. Hide Caption 16 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – Armed South Korean soldiers walk on a road near a military drill field in Paju on March 27. Hide Caption 17 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers ride in a military truck in Paju on March 27. Hide Caption 18 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – A B-52 bomber flies over the wire-topped fence of a U.S. air base in Osan, South Korea, on Tuesday, March 19. Hide Caption 19 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers take part in a drill to guard the building of a state-run telecom company in Seoul against potential guerrilla attacks on Thursday, March 14. Hide Caption 20 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean army soldiers jump off a military truck during a drill outside a U.S. airbase in Pyeongtaek as part of annual joint exercises with the United States on March 14. Hide Caption 21 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean Marines operate K-55 self-propelled howitzers on the western island of Ganghwa near the disputed maritime frontier with North Korea on Wednesday, March 13. Hide Caption 22 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean soldiers stand guard as a North Korean soldier, far center, looks on at the truce village of Panmunjom in the demilitarized zone dividing the two Koreas on March 13. Hide Caption 23 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – South Korean marines patrol on the South Korea-controlled island of Yeonpyeong near the disputed waters of the Yellow Sea on Tuesday, March 12. Hide Caption 24 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – In this Navy handout image taken on March 5, Lt. j.g. Matthew Harmon serves as helm safety officer aboard the guided-missile destroyer USS McCampbell during a replenishment at sea, part of Foal Eagle 2013, the joint exercises between the United States and South Korea. Hide Caption 25 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – Fire Controlman 2nd Class Jason Titcombe, left, hands Fire Controlman 2nd Class Joshua Clements ordnance aboard the destroyer USS Lassen in this Navy handout photo taken on March 5. Hide Caption 26 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – U.S. Navy Boatswain's Mate 3rd Class Brittany Chiles signals to an SH-60B Seahawk helicopter as it lands on the flight deck of the destroyer USS McCampbell on March 4 in the Pacific Ocean, in this Navy handout photo. Hide Caption 27 of 28 Photos: Photos: Militaries and Korean tensions Militaries and Korean tensions – This March 17 Navy handout image shows the destroyer USS John S. McCain, front; the Republic of Korea Navy destroyer ROKS Seoae-Yu-Seong-Ryong, center; and the destroyer USS McCampbell moving into formation in the waters off the Korean Peninsula during exercise Foal Eagle 2013. 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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.