Later, China also responded, calling for a peace settlement in regards to Korean Peninsula issues through dialogue.
North Korea has not commented on the launch.
South Korea and the United States last week chose to postpone joint military drills indefinitely amid a growing coronavirus outbreak in the South which has now infected soldiers from both countries.
"Kim's activities appear to be meant to highlight to his people that his campaign to build a self-reliant economy is business as usual while boosting military morale and also showing they were not affected by the virus", said Kim Dong-yup, a professor at Kyungnam University in Seoul.
The two devices were fired on Monday eastwards over the sea from the Wonsan area on the east coast, South Korea's Joint Chiefs of Staff said.
North Korea in previous years has intensified testing activity in response to springtime military exercises between South Korea and the United States that it has described as invasion rehearsals.
While the nature of the projectiles fired Monday wasn't immediately clear, it's the first such provocation since Kim said December 31 that he was no longer bound by a self-imposed freeze on major weapons tests.
North Korea has historically stepped up missile testing in the spring.
If confirmed as a missile test, the latest launches would be the first by Pyongyang this year since Kim Jong-un publicly warned in January that the world would soon see a "new strategic weapon" in the face of what he called the US' "hostile policy".
"It sounds like they are starting off with something small and conventional in nature", Joshua Pollack, a senior research associate at the Middlebury Institute of International Studies at Monterey, said, adding that South Korea's assessment that the test represented a continuation of the weekend's exercise "makes sense".
There have been recent signs of domestic political friction in North Korea.
"With the spread of the virus, North Korea has to strengthen its solidarity and convince its people", he said.
He said the communist state was no longer bound by a self-imposed moratorium on nuclear or long-range missile tests.
The new coronavirus has so far sickened more than 80,000 people and killed over 3,000 worldwide.
Experts have warned that North Korea, parts of which are impoverished, does not have adequate medical supplies to deal with a serious disease outbreak.
North Korea's borders have been effectively closed since late January, amid a nationwide campaign to prevent the spread of the coronavirus. During the latest test-firing on November 28 a year ago, two projectiles were launched from the DPRK's eastern province of South Hamgyong towards the eastern waters. Pyongyang has said the talks broke down as Washington came to the table "empty-handed".
North Korea analysts have previously suggested that the "strategic weapon" could mean an advanced type of the country's intercontinental ballistic missile (ICBM) or a submarine-launched ballistic missile (SLBM).
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