In a statement Tuesday, Park condemned the nuclear test, saying it harmed ties between the two Koreas.
North Korea announced last month that it was planning a new nuclear test and more long-range rocket launches, all of which it said were part of a new phase of confrontation with the United States.
It made the threats two days after the United Nations Security Council had approved the broadening of sanctions on the reclusive, Stalinist regime in response to the North's launching of a long-range rocket in December that apparently succeeded in putting a satellite in orbit.
Pyongyang said it carried out the launch for peaceful purposes, but it was widely considered to be a test of ballistic missile technology.
Threats against the U.S.?
The North's recent propaganda has used words and images that imply a threat to the United States, but analysts dismiss the prospect that Pyongyang is willing or able to carry out a military attack on U.S. soil.
The latest nuclear test is worrying in military terms, Chinoy said, "but does this mean they can drop a nuclear weapon on Los Angeles? Absolutely not. The notion that they are going to target the U.S. is way off the mark."
U.S. analysts say North Korea's first bomb test, in October 2006, produced an explosive yield at less than 1 kiloton (1,000 tons) of TNT. A second test in May 2009 is believed to have been about 2 kilotons, National Intelligence Director James Clapper told a Senate committee in 2012.
By comparison, the bomb the United States dropped on Hiroshima in 1945 was a 15-kiloton device.
The North's latest test on Tuesday suggests the country has made a notable step forward in terms of power, said Jeffrey Lewis, East Asia director at the James Martin Center for Nonproliferation Studies, part of the Monterey Institute of International Studies.
"They were pretty clear they were going to up the yield a lot," Lewis said, and it "looks like they've done that."
He also warned that Kim Jong Un's regime may not be ready to relinquish the headlines yet, suggesting that a second test remained a possibility and could happen within a few days.
In a commentary last week, the North's KCNA said that Pyongyang had "drawn a final conclusion that it will have to take a measure stronger than a nuclear test to cope with the hostile forces' nuclear war moves."
It didn't elaborate on what would be stronger than a nuclear test.