South Korea was still analysing the launch and did not immediately have confirmation whether there were any casualties or damage to North Korean property, military spokesperson Lee Sung-joon told a briefing.
South Korea's Joint Chiefs of Staff earlier said the North fired a short-range ballistic missile that flew about 600km and a second ballistic missile that flew about 120km, both from an area near the west coast.
Both were fired towards the north-east, it said.
The trajectory means the second may have fallen in an area close to the North's capital, Pyongyang, but Lee said the military was unable to comment further.
South Korea has said it watches the North's missile launches from the preparations stage and tracks the projectile in flight.
"We strongly condemn North Korea's missile launch as a provocation that seriously threatens peace and stability on the Korean Peninsula," the Joint Chiefs of Staff said in a statement, adding it shared information on the missiles with US and Japanese authorities.
"The South Korean military will maintain its capacity and posture to respond overwhelmingly to any provocation while closely monitoring North Korea's various activities under a strong South Korea-US joint defence posture."
The second missile on Monday would be the second failed launch in five days. South Korea's military said the North fired what appeared to be a hypersonic missile on Wednesday but it spiralled out of control and exploded.
The first missile fired on Monday appeared to be similar to the North's KN-23 short-range ballistic missile, which is believed to have been used by Russia against Ukraine.
North Korea is suspected of supplying ballistic missiles and artillery shells to Russia. Both countries deny it despite their pledges of military cooperation and a recently signed pact that includes promises of mutual military support.
South Korean officials have said North Korea's recent short-range ballistic missile launches may be intended to show its wares to potential buyers.
On Sunday, North Korea criticised a joint military exercise by South Korea, Japan and the United States held last month and warned of "overwhelming response" against such drills.
North Korea said last week it had successfully conducted an important test aimed at developing missiles carrying multiple warheads, a claim rejected by South Korea as "deception" to mask a failed launch.
Reuters
