"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.
'No more artificial negotiations'
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 that there are no plans to move toward direct talks, "because North Korea has shown no willingness to move in a positive direction."
On Sunday, Pyongyang 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 called the South's offer a "crafty trick" and "empty words without any content."
Kerry's trip finished 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.
Kerry said in Beijing over 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 that it was planning its third nuclear test and more long-range rocket launches as part of 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 the joint U.S.-South Korean military exercises in South Korea, prompted an intensification in the North's threats.