World Cup debutants Bosnia-Herzegovina kick-off their maiden campaign against Argentina in Rio de Janeiro on Sunday.
Argentina are one of the favourites to win the World Cup in Brazil, which would be their third in total and first since lifting the trophy in 1986 in Mexico.
Speaking ahead of the Group F curtain raiser at the Estadio Jornalista Mario Filho, Dzeko said an Argentina team boasting Lionel Messi were odds-on to progress deep into the tournament.
"Argentina are favourites, not just in our group. They can go a long way in the competition," said Dzeko.
"They have the best player in the world and it will be their chance to win this because it's in South America."
While Argentina are tipped to enjoy a successful tournament in South America, Bosnia-Herzegovina are also seen as an outside chance to surprise at their first-ever World Cup.
Bosnia-Herzegovina, who became an independent nation 22 years ago after breaking away from the former Yugoslavia, booked their place at the showpiece event having finished ahead of Greece in Group G in the UEFA section of qualifying.
Dzeko netted 10 goals en route to the World Cup finals and is determined to help his team past Argentina, Nigeria and Iran, and into the knockout rounds.
"It's our first time here," the Manchester City striker said. "But our target is to try to go to the next round and we'll do everything to try and achieve that.
"To go into the next round would be an amazing achievement for us and the country."
