Prosecutors investigating a corruption scandal that has plunged South Korea into its biggest political crisis in decades are seeking a warrant for the arrest of the acting head of Samsung, the country’s most powerful conglomerate, on bribery charges.

Special prosecutors alleged that Jay Y Lee, heir apparent to the Samsung group, had paid bribes totalling more than $36m (£30m) to Choi Soon-sil, a longtime friend of the country’s impeached president, Park Geun-hye, in return for business favours.

“The special prosecutor’s office, in making this decision to seek an arrest warrant, determined that while the country’s economic conditions are important, upholding justice takes precedence,” Lee Kyu-chul, a spokesman for the office, told reporters on Monday.

The involvement of the third-generation leader of South Korea’s richest chaebol – or family-run conglomerate – comes days after Park denied any wrongdoing over allegations that Choi fraudulently received tens of millions of dollars from South Korean companies, including Samsung, for two foundations she operated.

Lee, 48, who became the de facto head of the Samsung group after his father, Lee Kun-hee, suffered a heart attack in 2014, was also accused of embezzlement and perjury in the prosecution’s application for an arrest warrant.

Seoul’s central district court will hold a hearing on Wednesday morning to decide whether to approve the prosecutors’ request.

Lee is suspected of paying millions of dollars in bribes to a business and two foundations run by Choi, whose alleged secretive role at the apex of the South Korean administration has brought Park’s unpopular presidency to the brink of collapse.

Park was impeached in early December, with the country’s constitutional court due to rule on the impeachment vote’s validity by June. If it upholds the vote, Park will immediately leave office and new presidential elections will be held within two months.

Lee was questioned for 22 hours at the end of last week, as he became the latest high-profile name to be sucked into a corruption scandal that could see Park become South Korea’s first democratically elected president to be forced out of office.

Prosecutors are trying to establish if the money Samsung paid Choi was connected to a 2015 decision by the National Pension Service (NPS) to approve a controversial $8bn merger of two Samsung group affiliates.

The NPS supported the merger of Samsung C&T and Cheil Industries even though it was expected to create losses for the pension fund, according to the Korea Times. The merger was intended to enable Lee to increase his stake in the Samsung group and clear the way for a smooth transfer of power from his ailing father.

The chairman of the NPS, Moon Hyung-pyo, was arrested last month after he admitted ordering the fund – the world’s third biggest – to support the merger. At the time, Moon was head of the health ministry, which oversees the NPS.

The prosecutors’ indictment against Moon on charges of abuse of power and false testimony alleges that Park ordered him to realise the merger.

Samsung has acknowledged providing funds to the three institutions but on Monday it denied that Lee had paid bribes to facilitate the merger.

“It is difficult to understand the special prosecution’s decision,” the firm said in a statement. “We cannot accept the special prosecutors’ argument that there were unlawful favours related to the merger or the leadership succession.”

Lee’s possible prosecution is a fresh source of embarrassment for Samsung, whose reputation has already been damaged by fire accidents involving its faulty Galaxy Note 7 smartphone.

“The public demand that chaebol, especially Samsung, should not be an exception and that everyone should be equal before laws has become stronger,” said Kim Sang-jo, executive director of Solidarity for Economic Reform, a private business watchdog. “Prosecutors and judicial institutions cannot ignore the huge pressure from the public.”

Park, 64, is still president but has ceded her powers to an acting leader while the constitutional court deliberates over her impeachment.

She has repeatedly apologised for acting “naively” over her relationship with Choi, but denies seeking any personal gain.

Earlier this month, in her first public appearance since being impeached, Park dismissed allegations that she and Choi colluded to pressure businesses into contributing to the latter’s non-profit foundations as “fabrication and falsehood”. She added that she had been “set up” over claims that she ordered the government to support the Samsung merger.

Choi, 60, is suspected of using large sums paid by Samsung to fund her daughter’s equestrian training in Germany.

Choi, who is facing charges of fraud and abuse of power, repeated her denials of any wrongdoing during an appearance at the constitutional court on Monday. “Even if I knew, I could not have passed on any information because I have no knowledge about mergers or hedge funds, anything like that, in the first place,” she told the court.

She is also accused of meddling in state affairs, including advising Park on economic policy and South Korea’s relations with North Korea.

Choi admitted she had access to a former presidential aide’s email address containing official documents, but insisted that she only ever read Park’s speeches to gauge their “emotional expression”. She described the president, whom she has known for 40 years, as “a person without ulterior motives”.

The two first met in the 1970s after the death of Park’s mother during an assassination attempt on her father, Park Chung-hee, who was then South Korea’s president. Choi’s father, the leader of shady religious cult, emerged as Park’s mentor after Park Chung-hee was assassinated by his head of intelligence in 1979.

The former UN secretary general, Ban Ki-moon, is among those rumoured to be preparing to run for the presidential Blue House if the constitutional court upholds Park’s impeachment and ends her presidency several months shy of her full five-year term.

Ban currently trails former opposition party leader Moon Jae-in as favourite to replace Park, according to a poll published on Monday.