He is accused of committing perjury during a parliamentary hearing last month into the affair, they said.
Lee, chairman of Samsung Electronics and the son of the Samsung Group chairman Lee Kun-Hee, was being questioned over allegations of bribery, prosecutors said Wednesday.
He is also accused of committing perjury during a parliamentary hearing last month into the affair, they said.
"I am sorry for causing concern among the people over this incident", Lee said as he arrived at the office of the special prosecutor investigating the case.
Lee and his lawyer were greeted by scores of journalists as well as dozens of protesters waving banners and chanting "arrest Lee immediately" and calling him a "co-culprit" in the scandal.
Prosecutor's office spokesman Lee Kyu-Chul said they would decide whether to seek a court warrant to arrest him formally when his questioning is completed.
"We will, of course, also investigate accusations that vice chairman Lee committed perjury" during the parliamentary hearing, the spokesman told journalists.
Yonhap news agency quoted an unidentified investigator as saying the likelihood of prosecutors seeking an arrest warrant was "high".
Lee was named a criminal suspect in the widening investigation on Wednesday.
The scandal centres on Park's secret confidante Choi Soon-Sil, who is accused of using her ties to the president to coerce top firms into "donating" tens of millions of dollars to two non-profit foundations which Choi then used as her personal ATMs.
Samsung was the biggest contributor to the foundations.
It is also accused of separately giving millions of euros to Choi to bankroll her daughter's equestrian training in Germany.
Prosecutors have for months questioned Lee and other senior Samsung officials to determine whether Samsung bribed Park and Choi in order to win state approval for a controversial merger which it sought in 2015.
The merger of two Samsung group units -- Cheil Industries and Samsung C&T -- was seen as a crucial step towards ensuring a smooth third-generation power transfer to Lee Jae-Yong.
It was criticised by many, who said it wilfully undervalued Samsung C&T's stocks. But the National Pension Service (NPS) -- a major Samsung shareholder -- voted in favour of the deal and it eventually went through.
Prosecutors have raided multiple Samsung offices as well as the NPS in connection with the scandal. The fund -- the world's third largest pension fund -- is overseen by the welfare ministry.
A former welfare minister was arrested last month for allegedly pressuring NPS officials to vote in favour of the Samsung deal.
Last month, Lee Jae-Yong told a parliamentary hearing that he was unaware of Samsung's involvement in funding Choi's daughter's equestrian pursuits and lavish life in Germany and denied that his company was seeking to win government favours.
Prosecutors on Wednesday asked parliament to file a complaint against Lee for giving false testimony at the hearing.
Samsung officials reportedly argued that although they were coerced to offer money, they sought no favours in return and thus the payments were not a bribe.