Foreign Minister Ri Su Yong warned that North Korea will not be browbeaten by international sanctions
North Korea says it is prepared to stop its nuclear weapons testing - if the US suspends war games with South Korea.
Speaking in New York, North Korean foreign minister Ri Su Yong said the tests would be halted if the United States suspended the annual military exercises.
However, he defended his country's right to maintain a nuclear deterrent and warned that North Korea won't be browbeaten by international sanctions.
"If we continue on this path of confrontation, this will lead to very catastrophic results, not only for the two countries but for the whole entire world as well," he said.
"It is really crucial for the United States government to withdraw its hostile policy against the DPRK (North Korea) and as an expression of this stop the military exercises, war exercises, in the Korean Peninsula.
"Then we will respond likewise."
According to South Korean officials, the latest missile launch took place from a submarine northeast of the coastal town of Sinpo on Saturday afternoon.
North Korean TV showed images of its Supreme Leader Kim Jong-Un inspecting the submarine and others of what appeared to be a missile emerging from under water.
South Korea's Joint Chiefs of Staff said the ballistic missile flew for about 19 miles (30km). A typical submarine-launched ballistic missile has a range of nearly 200 miles, it added.
The US, which confirmed the launch, responded by limiting the travel of Mr Ri and his delegation to UN functions in New York as it views missile launches as a violation of UN resolutions.
Analysts say the launch from a submarine is a worrying development because mastering the ability to fire missiles from submerged vessels would make it harder for outsiders to detect what North Korea is doing before it launches, giving it the potential to surprise its enemies.
They point out that the latest belligerence comes before next month's ruling party congress, which could further cement Mr Kim's hold on power.
There are also concerns that Pyongyang is planning a fifth nuclear test, with South Korea's military on high alert for one to be carried out "at any time".
Satellite images suggest tunnel excavation may have resumed at the the Punggye-ri site, where the country's last three nuclear tests took place.