Vucic stressed during the conversation that Serbia sees Greece as a sincere friend, "and follows with great attention the goings on" in the economy sphere.
The two officials discussed cooperation in the fields of energy and trade, the government's media relations office said.
Kotzias said he arrived to Serbia as a friend, and that his country wants to help Serbia become an EU member state, and offers full support for the first negotiation chapters to be opened as soon as possible.
"Our experience in negotiations with the EU is good and we will be glad to share it. If we work together, we can help Europe be better in negotiations with Serbia," Kotzias said, adding that Tsipras could visit Serbia in July or September this year.
During the meeting, the officials concluded that the two countries will step up the cooperation in all fields, and agreed to form a joint technical group that will deal with economic issues.
It was also announced that Greece would support the holding of a Balkans conference on migration that should give the region an opportunity to find a common solution to the problem.
Earlier in the day, Kotzias met with his Serbian counterpart Ivica Dacic.