The country test-fired its second missile in one week after top US and South Korean diplomats met in Washington to condemn its nuclear ambitions.
A North Korean intermediate-range missile test failed immediately after launch early on Thursday, the US and South Korean militaries have said.
Shortly before the launch, US and South Korean top officials reached an agreement in Washington on strengthening their military and diplomatic cooperation against the North's nuclear and missile programmes, which are not in line with UN Security Council resolutions.
"We strongly condemn the North's continued illegal acts of provocation," South Korea's joint chiefs of staff said in a statement.
Japan was also swift to condemn the launch, saying that it would formally protest through its embassy in China's capital Beijing.
The missile was launched from the western city of Kusong during the final US presidential debate. It appears to have been an intermediate-range Musudan missile capable of reaching US bases as far away as Guam and any part of Japan.
It was the North's eighth attempt to launch the missile in the last seven months.
North Korea also attempted but failed to launch the same type of missile on Saturday, the US Strategic Command and South Korea's Office of the Joint Chiefs of Staff said.
The United States would do "whatever is necessary" to defend itself, South Korea, and other allies against North Korea, Secretary of State John Kerry said before the failed missile launch.