SEOUL (Reuters) -South Korea's Constitutional Court on Monday began reviewing the impeachment of President Yoon Suk Yeol over his Dec. 3 martial law proclamation, starting a process to decide if he will be removed from office, while investigators plan to question him this week on criminal charges.

The court will hold the first public hearing on Dec. 27, spokesperson Lee Jean told a news conference, after the court's six justices met to discuss plans for reviewing the impeachment by the opposition-controlled parliament on Saturday.

The court has up to six months to decide whether to remove Yoon from office or to reinstate him. The first hearing will be "preparatory" to confirm major legal issues of the case and the schedule among other matters, Lee said.

Yoon is not required to attend that hearing, she said.

In 2017, the court took three months to issue a ruling to strip then-President Park Geun-hye of the presidency following her impeachment for abusing the powers of her office.

Yoon and a number of senior officials also face potential charges of insurrection for the short-lived martial law.

A joint team from the police, the defence ministry and an anti-corruption agency are planning to call Yoon in for questioning at 10 a.m. (0100 GMT) on Wednesday in connection with the charges, a police official told Reuters.

The presidential security service declined to accept summons for Yoon to appear saying it was not in the position to do so, Yonhap news said. An anti-corruption agency said the summons was also sent by express registered mail.

The government, led by acting president Han Duck-soo, has continued to try to reassure international partners and investors, while political parties pledged to cooperate in efforts to stabilize the situation.

Early on Monday, the finance minister, Bank of Korea governor and top financial regulators met and pledged round-the-clock monitoring of financial and foreign exchange markets.

Yoon's surprise martial law declaration and the ensuing political crisis spooked markets and South Korea's diplomatic partners, worried over the country's ability to deter nuclear-armed North Korea.

PREPARING FOR TRUMP

Members of parliament have also raised concerns that the martial law debacle has been damaging at a time South Korea needs to be preparing for the second Donald Trump presidency in the U.S., the country's biggest ally.

Finance Minister Choi Sang-mok and ruling People Power Party floor leader Kweon Seong-dong discussed tackling economic challenges, including heightened uncertainty for the trade-dependent country created by Trump's pledge to hike tariffs.

Opposition Democratic Party leader Lee Jae-myung welcomed Trump's selection of his former intelligence chief to handle special missions including North Korea as a sign of commitment for dialogue to ease tensions.

Foreign Minister Cho Tae-yul said the nomination of Richard Grenell indicated North Korea will be one of the top priorities of Trump's presidency. Trump met North Korean leader Kim Jong Un on three occasions during his first term.

The benchmark KOSPI index fell on Monday, after last week's sharp gains prior to the impeachment, as traders were seen booking profit amid eased political uncertainty.

The Saturday impeachment vote passed with at least 12 members of Yoon's ruling party joining in favour, which has thrown the party into disarray with its leader Han Dong-hoon announcing his resignation on Monday.