Addressing a joint news conference alongside South Korean President Park Geun-hye, Obama said threats by North Korea will get it "nothing except further isolation" from the global community.
But Obama acknowledged there are limits to what impacts additional penalties can have on the country.
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Obama said the missile technology and nuclear weapons that North Korea is developing pose a direct threat to Korea and Japan, two very close US allies in the region, but to the United States as well.
"We can't waver in our intention. We have to make sure that, in strong concert with our allies, that we are continuing to press North Korea to change its approach," Obama said, presenting a united front in the presence of Park.
The White House said it was keeping close tabs on activity at North Korea's nuclear test site, where commercial satellite imagery this week showed increased activity.
Park said the assessment of her government is that North Korea is "fully ready now" to conduct another nuclear test. "This is a very tense situation," she said.
"President Obama's visit to South Korea sends a strong message to North Korea that its provocative acts cannot be tolerated," she said.
Obama also noted that his visit comes at a time of "great sorrow" for South Korea, which is mourning the loss of more than 300 people in a ferry that sank off the country's southwestern coast. The vast majority of the victims were high school students.
"So many were young students with their entire lives ahead of them," Obama said, invoking his two daughters, both close in age to many of the ferry victims. "I can only imagine what the parents are going through at this point, the incredible heartache."
He said he was donating a magnolia tree from the White House lawn to the high school in honor of the lives lost and a symbol of friendship between the US and South Korea.
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