"The FSS board members decided to terminate the contract with Curcic by mutual consent, while Milosevic resigned as the national team director at today's session," the Serbian Football Association said on its website (www.fss.rs).
"We thank Curcic for his efforts and wish him all the best in his future endeavours."
Former Aston Villa striker Milosevic was Curcic's most avid supporter within the FSS after the 44-year old took over from Dutchman Dick Advocaat in November, 2014.
Curcic failed to turn around Serbia's fortunes in a poor Euro 2016 qualifying campaign after Advocaat took one point from their opening three games.
Serbia finished the qualifiers fourth in their section with four points from eight matches, behind Portugal, Albania and Denmark.
Backing for Curcic dwindled further after tepid performances in a 1-0 defeat by Poland and a 1-0 win in Estonia in last month's friendlies.
Belgrade media were rife with speculation last week that the FSS had interviewed 62-year-old journeyman coach Slavoljub Muslin, who has managed 17 different clubs, to take over in a bid to reach the 2018 World Cup.
Serbia, who are in the same 2018 qualifying group with Wales, Ireland, Austria, Georgia and Moldova, have failed to advance to a major tournament since the 2010 World Cup.
"After a discussion with senior FSS officials, it was my assessment that the goal of qualifying for the 2018 World Cup lacks the right atmosphere and support," said Curcic.
"I wish to thank the players for their full commitment and those individuals who believed in my work, while I also hope Serbia will reach the tournament in Russia."
(Editing by Toby Davis)
