His 2-minute-long address comes just hours before the National Assembly is set to hold a vote on a motion to impeach the president.
Yoon apologized for "causing public concern and inconvenience" due to the declaration that shook the nation on Tuesday.
He also pledged that another such attempt would not happen again, reassuring the public about the possibility of a re-occurrence.
However, he did not provide detailed explanations about what led him to declare martial law and other suspicious allegations surrounding it. He simply said his decision was made out of "desperation as the country's leader."
Yoon instead made a dubious statement, saying that he would leave future decisions regarding state affairs including his presidential term to the ruling People Power Party (PPP).
The impeachment motion, proposed by six opposition parties including the main opposition Democratic Party (DP), requires a two-thirds majority or 200 votes in the 300-member National Assembly to pass.
The PPP has apparently decided to oppose the motion, but some of its members are expected to vote in favor of impeachment amid the party's internal strife.
Once passed, Yoon's duties will be suspended immediately and the Constitutional Court will begin deliberating the case.
Shortly after Yoon's brief address, the PPP's leader Han Dong-hoon said that Yoon is no longer capable of fulfilling his duties as president, saying that it is "inevitable" for Yoon to step down early.
The DP leader Lee Jae-myung, expressed disappointment over the last-minute apology, which came just before the impeachment vote.
"There is no way to resolve the situation other than Yoon's immediate resignation or an early departure through impeachment," he said.
The impeachment vote against the president is scheduled for 5 p.m. later in the day at the National Assembly, along with a separate vote to investigate allegations against first lady Kim Keon Hee.
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