By Jack Kim and Yun Hwan Chae
SEOUL (Reuters) - South Korean President Park Geun-hye faces a deepening crisis over allegations an old friend enjoyed inappropriate influence over her, a scandal that has sapped her support to an all-time low.
Park's popularity has slumped to 17.5 percent, the lowest since she took office in February 2013, according to a poll released on Thursday by pollster Realmeter.
Forty-two percent of people polled said Park should face impeachment or step down. Her conservative Saenuri Party saw its support rating overtaken by the main opposition Democratic Party, trailing by 4 percentage points at 26.5 percent.
Parliament began discussion on Thursday to appoint a special prosecutor to investigate the allegations amid calls from legislators for Park to reshuffle the presidential office and the cabinet.
It was not clear whether Park herself would be investigated.
Opposition parties have demanded a thorough investigation but have not raised the possibility of impeaching the president.
The South Korean won dropped to a near 4-month low as investors grew more concerned over the potential ramifications of the affair.
A public apology from Park on Tuesday for giving the friend, Choi Soon-sil, access to draft speeches during the first months of her presidency has done little to deflect demands that Park reveal the full nature of her ties with Choi and whether she enjoyed favors because of her friendship with the president.
Park, the daughter of a former president, Park Chung-hee, said she had consulted Choi with good intentions and Choi was someone "who gave me help when I was going through a difficult time".
Park is the latest South Korean leader to become engulfed in scandal involving family or friends, in the latter part of a single five-year term presidency.
None of the five democratically elected presidents before Park finished their terms with more than 30 percent approval.
Civic groups and students have called for Park to step down and for criminal charges against her aides and others who helped release government documents to Choi, who is not known to have held a government post.
Choi, in her first comments after weeks of reports about her ties with Park, told a newspaper she did get drafts of Park's speeches after Park's election victory but denied she had access to other official material, or that she influenced state affairs or benefited financially.
In an interview published on Thursday, Choi dismissed as "a work of fiction" reports she was a member of a group of women who used their links with the president to wield influence.
Media has speculated for weeks that Choi may have used her friendship with Park to play a role in the establishment of two foundations with contributions of about 50 billion won ($44 million) from conglomerates and that she had benefited from their operations.
Choi dismissed that speculation, denying she had benefited from government funds or control of state finances.
She said she had made changes to drafts of Park's speeches in the early days of her presidency.
"It was a wrong thing to do and I am sorry," Choi told the Segye Ilbo newspaper in the interview in Germany where she is staying.
Prime Minister Hwang Kyo-ahn said the government was doing everything to get to the bottom of the allegations surrounding Choi, including working with German authorities to determine her whereabouts and bring her back to South Korea.
The Segye Ilbo newspaper said it interviewed Choi in the German state of Hessen and she was too weak to travel to South Korea.
Media has published photographs of Choi with Park from 1979 when the president, the eldest daughter of then-President Park, was filling in as first lady after her mother was killed by an assassin who meant to kill her father.
Her father, who took power in a coup as a military officer, was shot dead by his disgruntled spy chief in 1979. Park, the current president, who is 64, has never married.
(Additional reporting by Christine Kim; Editing by Tony Munroe, Robert Birsel)