Some members of Yoon's conservative People Power Party (PPP) have urged the president and his wife, Kim Keon Hee, to apologise for the incident dubbed by local media "Dior bag scandal" and admit receiving the purse was, at least, inappropriate, in the hope of putting the matter to rest.
Yoon's office said it had no information to share.
By opting to remain silent and, at the weekend, pushing for the party leader to resign due to a disagreement over some members' stance, Yoon risks creating a flash point that could end up costing PPP the April 10 election, analysts say.
"It is a political bombshell," said Rhee Jong-hoon, a political analyst. "The Kim Keon Hee risks are only going to get bigger."
Yoon won a close election in 2022 but his PPP is a minority in the parliament, which is controlled by the rival Democratic Party.
Analysts said when Kim, as the spouse of a government official, accepted the purse, which had a price tag of 3 million won ($2,250), she may have violated an anti-bribery law.
The president's supporters say Kim is the victim of an illegal plot to set her up and a smear campaign.
The case surfaced in November when a YouTube channel aired a video clip secretly recorded by a Korean American pastor with a hidden camera as he visited Kim and handed her the handbag.
The pastor, Rev. Abraham Choi, who has been involved in religious exchanges with North Korea and is an advocate of engagement with Pyongyang, said he initially sought a meeting with Kim out of concern for Yoon's hardline North Korea policy.
Choi said while Kim was a family acquaintance, her response to discussions over possible luxury gifts - including Chanel cosmetics he claims he gave her in their first meeting - led him to believe such gifts were the only way to secure an audience.
"You might say they were like an entry pass, a ticket for a meeting (with Kim)," Choi told Reuters in an interview on Tuesday.
Yoon's office said it had no information to provide when asked about Choi's claims.
An unnamed presidential official told Yonhap news agency last week that Choi had deliberately approached Kim with the intention of illegally filming using his family connections, and that gifts to the couple are handled and stored as property of the government.
After a first meeting, Choi said he became concerned about Kim's role in the administration and worked with a reporter at the YouTube channel, which airs left-wing news and commentary, to film her accepting the pricey bag during a second visit.
"A normal person would then say, 'Reverend, I can't see you if you do this,'" he said. "But the First Lady gave me the place and time."
Kim also remains mired in allegations of stock price manipulation from about 12 years ago, a case for which opposition-controlled parliament voted last month to appoint a special prosecutor to investigate.
PPP opposed the bill as a plot by the DP to hamper an investigation into its leader, Lee Jae-myung, and his corruption charges, which he denies. Yoon vetoed the bill as politically motivated.
In 2021, Kim made a public apology after months of allegations of falsified professional record and plagiarism in her Ph.D. thesis overshadowed Yoon's campaign for president.
'MARIE ANTOINETTE'
A number of PPP members have argued public sentiment is focused on Kim and not the hidden camera sting, reflecting growing concern the issue is leaving a bad impression with voters.
Tension between Yoon's office and his party boiled over last week when a member of its leadership, Kim Kyung-yul, likened the situation to the notoriety of Marie Antoinette, the French Queen known for her profligacy.
Local news reports said Yoon was livid and wanted to remove the party's leader, Han Dong-hoon, marking at least a brief split between the president and an official widely seen as a protégé and close associate.
In a poll released by YTN cable news conducted this week, 69% of respondents said Yoon needs to explain his position regarding the controversy around the first lady.
Another poll by the financial publication News Tomato in December showed 53% of respondents believe Kim acted inappropriately, while 27% said she was caught in a trap set up to embarrass her.
"The general public thinks, 'Okay, it may be a trap, but why did she take it (the bag) anyway?'" said Shin Yul, political science professor at Myongji University.
