Following independence, Stankevičius, who had been a member of the Communist Party of Lithuania, joined its successor party, the Democratic Labour Party.[1][2] From September 1993 to July 1994, he served as Minister of Social Security and Labour under Prime Minister Adolfas Šleževičius.[1][2][4] From 1994 to 1996, he was Minister of Administration Reforms and Self-government Affairs.[1][2][3][4] On 15 February 1996, he was appointed prime minister by President Algirdas Brazauskas, a position he held until 27 November 1996, a little more than nine months total.[1][2][3][4]
After leaving the office of prime minister, Stankevičius was elected to the Seimas, the Lithuanian parliament, where he served until 1998.[1][3] While in the Seimas, he served on the Committee on Social Affairs and Labour.[1] From 1998 to 1999, he served as Minister of Health under President Valdas Adamkus and Prime Minister Gediminas Vagnorius.[1][3][4] In 1999, he retired from politics, residing in Vilnius.
Stankevičius died of natural causes on 17 March 2017 at the age of 81.[2][3][4] His body was laid out in Vilnius on 20 March, and the funeral took place at Antakalnis Cemetery the next day.