Speaking at a joint news conference, Dacic said one should "turn to good neighbourliness, seek what connects us and not what separates us."
He said it was very important for the two countries to participate in third markets together and intensify cooperation in transport, energy and the engineering industry.
Bevanda described his visit to Belgrade as "extremely important", saying that people in responsible positions in the region did not need mediators because they were educated and capable enough to communicate.
The two premiers talked about cooperation in the European integration process, refugee return and border issues.
Bevanda said there were four contentious points on the Serbian-Bosnian border. "We will leave it up to the experts on both sides to come up with a definition and then we will discuss it on the political level."
Dacic thanked Bevanda for Bosnia and Herzegovina's position on Kosovo, whose independence Bosnia has not recognised.
The two prime ministers agreed the Serbian and Bosnian governments should meet twice a year to discuss mutually important issues.
An extradition agreement is expected to be signed today in a bid to facilitate the fight against organised crime and corruption.
Radio and Television Serbia reported that Bevanda also met with Serbian Parliament Speaker Nebojsa Stefanovic but no details were revealed.