Striking an even harsher tone than Obama, Park also suggested any test would trigger an undesirable nuclear arms race in the region and render further nuclear negotiations pointless.
North Korea will get "nothing except further isolation" if it proceeds with its test, Obama said at a joint news conference in Seoul. But he also acknowledged there are limits to what effects additional penalties can have on the country.
"North Korea already is the most isolated country in the world, by far," Obama said. "Its people suffer terribly because of the decisions its leaders have made. And we are not going to find a magic bullet that solves this problem overnight."
Still, he said it's important to look at new ways to pressure North Korea, including applying sanctions that have "even more bite."
Park added that such a test would bring "fundamental change" to the region's security landscape and trigger a nuclear arms race as countries hurry to match the North's nuclear capabilities. She said such an outcome would make it fruitless to resume negotiations with North Korea aimed at getting it to abandon its nuclear weapons and its nuclear program.
In 2009, North Korea walked away from six-party talks with the U.S., South Korea, Japan, Russia and China that offered financial incentives in exchange for denuclearization.
Park said her government has assessed that the North is "fully ready now" to conduct another nuclear test.
"This is a very tense situation," she said through a translator. "President Obama's visit to South Korea sends a strong message to North Korea that its provocative acts cannot be tolerated."
Obama said the missile technology and nuclear weapons that the North is developing pose a direct threat to South Korea and Japan, two staunch U.S. allies in the region, as well as to the United States.
"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.
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 also called on China to use its influence to dissuade North Korea from going ahead with the test. China is North Korea's closest ally in the region.
Touching on another sensitive regional issue, Obama gave voice to South Korea's grievances with Japan by calling Japan's use of Korean "comfort women" during World War II a terrible and egregious violation of human rights. Historical issues have become a major rift between two of the staunchest U.S. allies in Asia, and Obama has taken on the task of trying to bring the two sides closer.
"Those women were violated in ways that even in the midst of war was shocking," Obama said. "They deserve to be heard, they deserve to be respected."
At the same time, he said Japanese Prime Minister Shinzo Abe recognizes that the past must be acknowledged in full. Obama urged both Japan and South Korea to move beyond the heartache of the past, noting that their interests "so clearly converge" on other fronts.
Obama arrived in South Korea on Friday morning, a little more than a week after a ferry carrying more than 300 people, most of them students from one high school near Seoul, sank off the country's southwestern coast. He noted that he was visiting at a time of "great sorrow" and offered America's deepest condolences.
"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 that were lost and as a symbol of decades of friendship between the U.S. and South Korea.
After arriving at the Blue House, Park's official residence, Obama presented her with an American flag that he said flew atop the White House on April 16 — the day the ferry began to list. He also called on the U.S. and South Korean delegations to observe a moment of silence in honor of the victims.
Most of the ferry's 29-person crew survived, but 11, including the captain, have been arrested on suspicion of negligence or abandoning people in need as the ferry sank. Park recently blasted their actions as "tantamount to murder."
Accepting the flag, Park drew a parallel between the way Americans pulled together after 9/11 and the resilience of South Koreans following one of the worst maritime disasters in her country's history.
"The Korean people draw great strength from your kindness," she said.
After a working dinner with Park, the president was to spend the night in South Korea, the second stop on a four-country Asia swing that includes visits to Malaysia and the Philippines.
Associated Press writers Nedra Pickler and Josh Lederman in Washington contributed to this report.
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