The US president also said he wanted to "break that pattern" of North Korea creating a crisis and then being rewarded with incentives in order to get it to back down.
And he reinforced the US's commitment to defending South Korea, saying the US would maintain a "robust defence posture".
"Prestige and security and prosperity are not going to come through the path of threatening neighbours and engaging in violations of international law,'' Obama said.
Lee, meanwhile, said that South Korea, along with the US, Japan, China and Russia, would seek new measures designed to compel the North to "irrevocably dismantle all of their nuclear weapons programmes".
The United Nations Security Council last week voted unanimously to impose further sanctions on the country following its second nuclear test on May 25.
US officials have said that the North Koreans appear to be making preparations for a third nuclear test.
North Korea also said it would consider efforts to enforce UN sanctions as an act of war.