For most of his political career, Džamić has been a member of the Socialist Party of Serbia (Socijalistička partija Srbije, SPS).
He attended secondary school in nearby Trstenik, graduated from the University of Niš Faculty of Law, and later passed the bar exam in Belgrade.
[2] In 1990, he presided over a major event in which the television program Jeux sans frontières held competitions in the municipality.
[12] Džamić was re-elected to the Vrnjačka Banja assembly in the 1996 Serbian local elections; the SPS won a narrow majority in the municipality, and he was chosen afterward for another term as mayor.
[15][16][17] Džamić was the mayor of Vrnjačka Banja during the Kosovo War and the NATO bombing of Yugoslavia in early 1999; during this time, the municipality lost much of its regular tourist revenue and became a refugee centre for people fleeing bombardment in other communities.
[18] Later in the year, the opposition Alliance for Change group led a series of protests throughout Serbia against Slobodan Milošević's regime and the continued rule of the SPS.
Džamić did not take this approach in Vrnjačka Banja; it was noted that he voluntarily agreed to "sit in the dock" and respond to citizens' questions.
[19] In early 2000, Džamić was temporarily placed on an international sanctions list and forbidden from travelling to European Union countries.
The DOS also defeated the SPS in Vrnjačka Banja in the concurrent 2000 Serbian local elections, and Džamić's second tenure as mayor came to an end.
[26] The direct election of mayors proved to be a short-lived experiment and was withdrawn in the next local electoral cycle four years later.
Serbia's electoral system was again reformed in 2011, such that all mandates were awarded to candidates on successful lists in numerical order.
The SNS formed a coalition government that held sixteen out of thirty-one seats in the local assembly after the 2012 election, and the SPS was initially in opposition.
[44] Under the new governing arrangement, Džamić was again chosen as assembly president in September 2012 and remained in this role for the remainder of the term.