Opponents of South Korea's ousted leader, Park Geun-hye rallied in the capital, Seoul, on Saturday to demand that she be arrested, a day after she was thrown out of office over a corruption scandal involving the country's conglomerates.

The Constitutional Court ruling on Friday to uphold a parliamentary vote to impeach Park infuriated hundreds of her supporters, two of whom were killed as they tried to break through police lines outside the court. A third man, aged 74, had a heart attack and died on Saturday, a hospital said.

Park's critics were out in central Seoul on Saturday, where they have been gathering every weekend for months, while the former president's conservative supporters also took to the streets not far away, though fewer in number.

Police were out in force with riot shields but there were no reports of trouble.

"Impeachment is not the end. We've not dispersed, we're still going forward, united," said one anti-Park protester who gave his name as T.H. Kim.

"She's a citizen now. If she's done something wrong, she has to be arrested."

Park, 65, is South Korea's first democratically elected leader to be forced from office. Her ouster followed months of political paralysis and turmoil over a corruption scandal that also landed the head of the Samsung conglomerate in jail and facing trial.

The court ruling marked a dramatic fall from grace of South Korea's first woman president and daughter of Cold War military dictator Park Chung-hee. She served as his first lady after the 1974 assassination of her mother.

At times, Park and her supporters have bridled at associating her with her father, who seized power in a 1961 coup and ruled for 18 years until he was gunned down by his security chief in 1979.

Though she has spent years in the public eye, she has remained an enigma.

Now, having lost presidential immunity, she could face criminal charges over bribery, extortion and abuse of power in connection with allegations of conspiring with her friend, Choi Soon-sil. Both women denied wrongdoing.

Park did not appear in court on Friday and did not make any comment after the ruling. She spent the night in the presidential Blue House though would leave at some time and return to her Seoul residence, a spokesman said.

Choi In-sook, a spokeswoman for protesters opposed to Park, told Reuters they were also demanding the resignation of acting president Hwang Kyo-ahn.

Prime Minister Hwang, a Park loyalist, became acting president when parliament voted to impeach her on 9 Dec.

Hwang has called for calm and promised that a snap presidential election, which has to be held within 60 days, would be smooth.

The chairman of the National Election Commission, Kim Yong-deok, said the vote would be free and fair and held by 9 May at the latest.

He said he was concerned differences could lead to an "overheated" atmosphere and called on the public to overcome conflict.

Park's supporters want her to stay in power. Some want the court decision overturned and her case heard again by new judges.

"We strongly request the trial is held again," said Chung Kwang Yong, a spokesman for organisers of rallies backing Park.

Leading in opinion polls to succeed her is prominent liberal politician, Moon Jae-in, who advocates reconciliation with North Korea.

Relations with China and the United States could dominate the presidential campaign, after South Korea this month began deployment of the U.S. THAAD missile defence system in response to North Korea's stepped up missile and nuclear tests.

Beijing has vigorously protested against the deployment, fearing its radar could see into its missile deployments. China has curbed travel to South Korea and targeted Korean companies in the mainland, prompting retaliatory measures from Seoul.

Reform of the country's giant conglomerates, known as "chaebol", will also be an election issue.

Park was accused of soliciting bribes from the head of the Samsung Group, the country's largest conglomerate, for government favours.

Samsung Group leader Jay Y. Lee has been accused of bribery and embezzlement in connection with the scandal and is in detention. His trial began on Thursday.

He and Samsung have denied wrongdoing.