The prosecution team's spokesman Lee Kyu-chul said Sunday that the Samsung vice chairman and two other group executives also will be summoned Monday morning.
Prosecutors will decide whether to again seek an arrest warrant for Lee by next week, after collecting additional information from Monday's investigation, the prosecution spokesman said.
Samsung chief Lee Jae-yong is being questioned for a second time as a suspect in South Korea's biggest political corruption scandal.
The 48-year-old is effectively in control of the conglomerate because his father, Samsung's ailing Chairman Lee Kun-hee, suffered a heart attack in 2014. A Seoul court rejected the arrest warrant for the vice chairman on January 19.
"I will faithfully tell the truth...today as well", Lee told reporters as he arrived at the prosecutor's office, the Korean Yonhap news agency quoted him as saying.
At the parliamentary hearing, Samsung admitted giving a total of 20.4bn won (£16m; $17.46m) to the two foundations, but denied seeking favours in return. The investigators also want to question Park in person, but have yet to agree with her office on how and when to do it.
Lee faces charges of bribery and embezzlement for allegedly orchestrating or knowing about bribes paid by Samsung Electronics to Choi Soon-shil, a friend of President Park Geun-hye, to get support for a controversial merger.
Until then she remains formally president but stripped of her powers, which are handed to the prime minister, a presidential appointee.