Court ruling in the case is expected on August 25th, a couple of days before Lee's ongoing period of detention ends.
"It is a typical corruption crime stemming from a back-scratching alliance between politics and business, which has indeed compromised our constitutional values", Special Prosecutor Park Young-soo was quoted by Yonhap News Agency as telling Seoul Central District Court.
Park also is on trial for more than 18 charges.
They are seeking terms ranging from seven to 10 years for his co-accused.
Lee Jae-yong is accused of bribing Park's powerful confidante Choi Soon-Sil with millions of dollars to win presidential favours and ease a controversial 2015 merger deal.
The undertrials had continued false statement and excuse during the past court hearings that lasted for over five months, according to the special prosecutors. "I have never asked anyone, including the president, for anything for the company or my personal gain", he said.
Samsung Electronics offered no comment regarding the prosecutors' demand.
Lee, the third-generation Samsung heir, was brought into custody on February 17 and was indicted 11 days later on five charges of bribery, embezzlement, perjury, hiding assets overseas and concealing the proceeds of criminal acts.
South Korean police on Monday raided a management office for residences of Samsung Electronics Chairman Lee Kun-hee and his family over alleged misappropriation of company funds used to pay for interior renovations, they said.
He also claimed to have had no role in wider decision-making at Samsung and "mostly listened to other executives".
Semiconductors and display continue to provide Samsung's strongest growth.
The independent counsel believes the money was in exchange for Park's support and to secure the vote of the state-run National Pension Service, a major stakeholder in Samsung C&T.in favor of merging with another branch of Samsung Group, Cheil Industries.