SPS executive member (2000) Đukić was elected to the executive committee of the Socialist Party in February 2000, when the party dominated Serbian politics. He ran for the
Belgrade city assembly in
Savski Venac's second constituency seat in the
2000 Serbian local elections later in the year. Savski Venac was an opposition stronghold, and he was defeated by
Zoran Šami of the
Democratic Opposition of Serbia (DOS) amid a landslide DOS victory. SPS leader
Slobodan Milošević was defeated in the
2000 Yugoslavian presidential election and subsequently fell from power in the
5 October Revolution, a watershed moment in Serbian politics. After Milošević's fall, Đukić withdrew from direct political activity for a number of years.
SPS candidate (2016–20) Đukić appeared in the seventy-fourth position on the SPS's
electoral list in the
2016 Serbian parliamentary election and the eighty-fourth position in the
2020 parliamentary election. The party's lists won twenty-nine and thirty-two seats, respectively, and he was not elected on either occasion. He was given the eleventh position on the SPS list in the
2018 Belgrade city assembly election. The list won eight mandates, and he was not elected. He had the opportunity to enter the assembly as the replacement for another party member on 7 June 2018, but he declined.
Parliamentarian (2022–24) Đukić was promoted to the sixth position on the SPS's list in the
2022 parliamentary election and was elected when the list won thirty-one seats. The SPS continued its participation in a
coalition government led by the
Serbian Progressive Party (SNS) after the election, and Đukić supported the administration in the assembly. He was a member of the health and family committee, a deputy member of the education committee, the leader of Serbia's parliamentary friendship group with
Morocco, and a member of the friendship groups with
China,
Cyprus, the
Czech Republic,
Egypt,
Germany,
Iceland,
Russia, the
United Kingdom, and the
United States of America. It was rumoured that he would be appointed as Serbia's health minister in 2022, but this did not happen. Đukić appeared in the largely ceremonial 110th position (out of 110) on the SPS's list in the
2023 Belgrade city assembly election. Election from this position was a mathematical impossibility, and he was not elected when the list again won eight seats. He was given the thirty-first position on the SPS's list in the
2023 parliamentary election and was not re-elected when the list fell to eighteen seats. His term ended when the new assembly convened in February 2024. He may have the opportunity to re-enter the assembly as the replacement for another SPS delegate at some time in the current assembly's term. ==Electoral record==