Ivković was a supporter of Serbian president Slobodan Milošević in the 1990s. In December 1996, amid large-scale protests against Milošević's rule in Belgrade and throughout the country, he was prominent in organizing a pro-Milošević counter-protest at the Terazije fountain.[3]
He later joined the SNS and supported Aleksandar Vučić's candidacy in the 2017 Serbian presidential election.[4] He appeared in the forty-sixth position on the party's electoral list in the 2018 Belgrade City Assembly election and was elected when the list won a majority victory with sixty-three out of 110 seats.[5][6] He served for the next four years as a supporter of the city government.
Ivković was given the tenth position on the SNS's list in the 2022 Serbian parliamentary election and was elected when the list won a plurality victory with 120 out of 150 seats.[7] In his first term, he was a member of the assembly's culture and information committee, a deputy member of the committee on the diaspora and Serbs in the region, the leader of Serbia's parliamentary friendship group with Mali, and a member of the friendship groups with Greece, Montenegro, and Slovenia.[8]
He received the twenty-fifth position on the SNS's list in the 2023 parliamentary election and was re-elected when the list won a majority victory with 129 seats.[9] He is now a member of the culture and information committee, the committee on human and minority rights and gender equality, and the parliamentary friendship group with Greece.[10]