South Korean authorities have imposed a travel ban on President Yoon Suk Yeol, who is under investigation for his short-lived martial law declaration last Tuesday.

Yoon narrowly survived an impeachment motion against him over the weekend, after MPs from his ruling People Power Party (PPP) boycotted the vote.

PPP members said they had decided not to support the motion after Yoon agreed to shorten his term and not get involved in foreign and domestic affairs.

However, the opposition Democratic Party, which commands a majority in the parliament have criticised the deal, with floor leader Park Chan-dae calling it "an illegal, unconstitutional second insurrection and a second coup".

Tens of thousands of people have come out in protest since Yoon's short-lived martial law order, calling for him to resign or be impeached.

Since then, despite the failed impeachment motion, several key figures involved in the martial law order have also seen action taken against them.

Former Defence Minister Kim Yong-hyun, who reportedly proposed the martial law declaration to Yoon, was arrested on Sunday. He had earlier resigned on Wednesday after apologising and saying he would take "full responsibility".

Travel bans have been placed on Kim, Lee, Defence Counterintelligence Commander Yeo In-hyung, and Army Chief of Staff Park An-su.

Many others have stepped down from their posts.

These include former Interior Minister Lee Sang-min who resigned on Sunday, saying he would take responsibility for "failing to serve the public and the president well".

And on Wednesday, senior aides of Yoon's office, including his chief of staff, tendered mass resignations hours after the martial law declaration was lifted.

Opposition calls PPP proposal a 'second coup'

In a public address on Sunday, PPP leader Han Dong-hoon said Yoon will no longer be involved in foreign and domestic affairs until his early resignation - adding that Prime Minister Han Duck-soo would manage government affairs in the meantime.

"The President will not be involved in any state affairs including diplomacy before his exit," said party leader Han.

However, Democratic Party floor leader Park Chan-dae described the proposed plan as "an illegal, unconstitutional second insurrection and a second coup".

Representative Kim Min-seok of the Democratic Party similarly criticised the plan, saying "nobody gave" PPP leader Han the power to make such decisions.

"The prime minister and the ruling party's announcement that they would jointly exercise the powers of the president, which no one has given them, is clearly unconstitutional," he said, according to a report on The Korea Herald.

The Ministry of National Defence confirmed at a briefing on Monday that the president retains command of the armed forces. That means in the event of any foreign policy incidents, including any possible threat from North Korea, Yoon is still, in theory, able to make executive decisions.

"The president can take the lead again any time he changes his mind," political science professor Shin Yul of Myongji University told The Korea Herald.

"No one will be able to stop him, if Yoon insists."

On Saturday Yoon apologised to the nation in what was his first appearance since the martial law declaration. He pledged not to impose another martial law order, and apologised for the "anxiety and inconvenience" he had caused.

However, the opposition has insisted that they "will not give up" on impeaching Yoon and has vowed to hold impeachment votes against Yoon every Saturday.

"We will definitely return this country to normal by Christmas and the end of the year and give it to you as a Christmas and end-of-year gift," Democratic Party leader Lee Jae-myung told a disappointed crowd after Saturday's failed impeachment attempt.

He again urged Yoon to resign on Monday, telling a press conference that Yoon's actions were "destroying" South Korea and its economy.