South Korea's constitutional court has begun trial proceedings for the impeachment of President Yoon Suk Yeol, who was suspended for declaring martial law and plunging his country into political turmoil.

MPs voted to impeach Yoon last Saturday, after his actions sparked widespread protests calling for him to step down.

The court now has six months to decide whether to remove Yoon or reinstate him.

Yoon's ruling People Power Party (PPP) has been grappling with the fallout ever since, with its leader announcing his resignation on Monday.

While public hearings for Yoon's impeachment trial could take months, the court is under pressure to decide quickly and bring an end to political uncertainty. Protesters have vowed to keep up their calls for Yoon's removal during court proceedings.

In the previous two instances a South Korean president faced impeachment, the court reversed one decision and upheld the other.

There had been questions on whether the trial could proceed in Yoon's case, as the court currently only has six justices out of nine. Three retired recently and have yet to be replaced.

But the court said on Monday it could run Yoon's trial with just six judges, and set a preliminary hearing date for 27 December.

If the court upholds impeachment in Yoon's case, the country must hold fresh presidential elections within 60 days. In the meantime, Prime Minister Han Duck-soo is serving as acting president.

It is unclear if Yoon will take the stand himself during the court hearings.

He ignored a summons to meet prosecutors in Seoul on Sunday, and is set to be ordered in again for questioning. If he fails to come forward this week, police may move to arrest him.

Yoon has defended his decision to impose martial law, and after his impeachment he once again said he would fight until the end.

Minutes after the constitutional court convened on Monday morning, PPP leader Han Dong-hoon announced his resignation.

"I sincerely apologise to all the people who are suffering from this emergency situation," Han said in a televised press conference.

Han has faced growing calls for his resignation particularly from the large pro-Yoon faction of his party, following the president's impeachment.

Han had initially tried to stage an orderly exit for Yoon. But when it became clear that Yoon was not backing down, Han did an about-face and called for his impeachment, saying it was the only way to remove him from office.

On Saturday, 12 PPP lawmakers were believed to have voted for impeachment, enabling the motion to pass. But most of the other PPP lawmakers voted against Yoon's impeachment.

All five Supreme Council members of the PPP said after the vote that they would resign - which would automatically dissolve the party leadership.

As the Supreme Council has been "destroyed", Han said, it was now "impossible" to serve his duties as party chief.

"While it pains me to think of my heartbroken supporters, I don't regret it," Han said, in reference to his decision to call for Yoon's impeachment.