Serbia have often been jeered by their own fans in home games at Red Star's Marakana stadium and Kolarov said the national team had been happy to move to the northern city of Novi Sad, where they thrashed Wales 6-1 last month to go top of Group A on goal difference.
"It was a great experience in a cracking atmosphere although the stadium only holds 13,000 fans and we were in two minds where we should play our match against the Belgians," the Manchester City left back said.
"All we want is unreserved support from a full house in Belgrade when we lock horns with Belgium because we will need our home crowd to act like an extra man on the pitch."
Serbia coach Sinisa Mihajlovic said after beating the Welsh that he would prefer to play Belgium in Novi Sad, but the fixture could not be moved from Belgrade at short notice.
Mihajlovic criticised Red Star fans for picking on the club's former goalkeeper Vladimir Stojkovic, who joined Partizan in 2010 following spells with a myriad of European clubs after he left Red Star in 2006.
Stojkovic was attacked by Red Star fans during Serbia's Euro 2012 qualifier against Italy in Genoa, when they stormed the team bus with burning flares.
Amid a string of bloody clashes over the last 20 years in Belgrade derbies, Red Star and Partizan fans have deprived the national team of support during home games when they have been too busy insulting each other and the players.
Kolarov, who played for OFK Belgrade before he joined Serie A side Lazio in 2007 and then moved to City in 2010, said: "I spoke about it to my team mates at City and none of them could understand how someone is capable of not supporting their country.
"Teams which have never made it to a major tournament have stronger support than we do and the time has come for fans in Belgrade to forget about their divisions and breathe like one to put wind in our sails.
"We have to be strong and in order to be strong we must feel like a team of eight million, otherwise reaching the 2014 World Cup in Brazil will remain a distant dream."
Serbia, Belgium and Croatia top the group with four points each from two games and the outcome of Serbia's encounter with Belgium, when Kolarov is likely to face his Manchester City captain Vincent Kompany, could have an impact.
The Serbians visit neighbours Macedonia on Oct. 16, when Belgium are at home to Scotland and Croatia entertain Wales.
- Manchester City