Here are the latest developments, from the NYU Times.
"President Yoon Suk Yeol of South Korea said he would lift the emergency declaration of martial law he imposed on Tuesday as soon as he could convene his cabinet, bowing to pressure after the National Assembly passed a resolution demanding it end. By law, Mr. Yoon needs to convene his cabinet to lift martial law.
The announcement by Mr. Yoon early Wednesday in South Korea came five hours after he declared martial law late Tuesday night in an unannounced televised address, and soon after the assembly unanimously voted to rescind it, a swift rebuke of the president’s response to the political deadlock that has hobbled his tenure.
Mr. Yoon’s declaration of martial law had banned “all political activities” and enabled him to take command of the news media, and drew thousands of protesters outside the assembly complex in what were largely peaceful demonstrations.
Mr. Yoon, who is deeply unpopular, accused the opposition of plotting an “insurgency” and “trying to overthrow the free democracy.” But his declaration, in an unannounced speech to the nation, was a dramatic escalation of a simmering political feud, and within hours had drawn protesters, tanks and military vehicles onto streets.
The South Korean act on martial law states that if the assembly demands an end to it, the president must lift it “without delay.” It was the first time a South Korean president had declared martial law since military dictatorship ended in the country in the late 1980s."
NOTE: There is no provision in US law for the Congress to reject martial law once it's declared by the President or a Governor. See below.