In a joint news conference in the East Room of the White House, Obama lauded Park Geun-hye, who took office this year amid sabre-rattling by North Korea, for displaying "calm and steady resolve in dealing with "threats and provocations that would test any nation."
Obama said the countries would keep modernizing their security alliance.
"We are on track for South Korea to assume operational control for the alliance in 2015," he said. "And we're determined to be fully prepared for any challenge or threat to our security. And obviously that includes the threat from North Korea.
"If Pyongyang thought its recent threats would drive a wedge between South Korea and the United States, or somehow garner the North international respect, today is further evidence that North Korea has failed again.
"President Park and South Koreans have stood firm, with confidence and resolve. The United States and the Republic of Korea are as united as ever. And faced with new international sanctions, North Korea is more isolated than ever. In short, the days when North Korea could create a crisis and elicit concessions -- those days are over."
Obama said the United States and South Korea stand ready to engage in diplomatic talks with North Korea "and, over time, build trust."
"But as always -- and as President Park has made clear -- the burden is on Pyongyang to take meaningful steps to abide by its commitments and obligations, particularly the denuclearization of the Korean Peninsula," Obama said.
Park said she and Obama had "a heart-to-heart talk" on "a wide range of common interests."
"First of all, the president and I shared the view that the Korea-U.S. alliance has been faithfully carrying out its role as a bulwark of peace and stability on the Korean Peninsula and in Northeast Asia, and that the alliance should continue to serve as a linchpin for peace and stability on the Korean Peninsula and in Asia.
"In this regard, I believe it is significant that the joint declaration on the 60th anniversary of our alliance we adopted spells out the direction that our comprehensive strategic alliance should take.
"Next, the president and I reaffirmed that we will by no means tolerate North Korea's threats and provocations, which have recently been escalating further, and that such actions would only deepen North Korea's isolation.
"The president and I noted that it is important that we continue to strengthen our deterrence against North Korea's nuclear and conventional weapons threat, and shared the view that in this respect, the transition of wartime operational control should also proceed in a way that strengthens our combined defense capabilities and preparations being made toward that way as well.
"We also shared the view that realizing President Obama's vision of a world without nuclear weapons should start on the Korean Peninsula and we stated that we would continue to strongly urge North Korea, in close concert with the other members of the Six-Party talks and the international community, to faithfully abide by its international obligations under the September 19th Joint Statement and the relevant Security Council resolutions."
"I take this opportunity to once again send a clear message: North Korea will not be able to survive if it only clings to developing its nuclear weapons at the expense of its people's happiness."
Asked if she thinks the North's Kim Jong-un has taken the U.S. and South Korean warnings seriously, Park said North Korea's isolation makes it "hard to find anyone that could really accurately fathom the situation in North Korea."
"Its actions are all so very unpredictable," she said.
She added there is "no knowing for sure" why the North has de-escalated its provocations in recent days, but "what is clear" is the international community "must speak with one voice" in telling the North it must abide by international standards.
Obama said the two countries have agreed to move ahead with implementation of their trade agreement, "which is already yielding benefits for both our countries."
"On our side, we're selling more exports to Korea -- more manufactured goods, more services, more agricultural products," Obama said. "Even as we have a long way to go, our automobile exports are up nearly 50 percent, and our Big Three -- Ford, Chrysler and GM -- are selling more cars in Korea.
"And as President Park and I agreed to make sure that we continue to fully implement this agreement, we believe that it's going to make both of our economies more competitive. It will boost U.S. exports by some $10 billion and support tens of thousands of American jobs.
"And obviously it will be creating jobs in Korea as they are able to continue to do extraordinary work in expanding their economy and moving it further and further up the value chain."
The U.S. president said the countries would keep pursuing its clean energy partnerships "to enhance our energy security and address climate change" while working on a new civilian nuclear agreement."
U.S. officials said Monday North Korea removed two BM-25 Musudan intermediate-range ballistic missiles after three weeks from their launch sites on the coast of the Sea of Japan.
Pentagon spokesman George Little said earlier in the day the North's rhetoric had toned down in recent weeks, calling it a "provocation pause."
Pyongyang's provocative behavior had been going on for much of the past three months.
On Feb. 12 it conducted North Korea's third underground nuclear test since 2006. This prompted U.S. and South Korean war games and U.S.-backed U.N. Security Council sanctions tightening -- both of which led to bellicose rhetoric from North Korea, including threats of nuclear strikes on U.S. territory.
At the end of March North Korea said it considered the Korean Peninsula back in "a state of war."
In April, as part of the growing tension between the two Koreas, North Korea withdrew its 53,000 workers from industrial park on its territory it runs with the South.
Pyongyang later rejected Seoul's offers of talks and South Korea last week pulled out its 175 remaining factory managers from the facility, ending the only remaining symbol of cooperation between the two countries.
The White House meeting celebrates the 60th anniversary of a U.S.-South Korean mutual defense. The treaty, worked out in the months after the Korean War's July 27, 1953, cease-fire armistice was signed.