Speaking at a joint news conference, Pusic said Croatia supported Serbia's European integration, as it had made big progress.
Vucic thanked Pusic and her associates for the support and "the moment chosen to visit Belgrade", only a few days before Croatia joins the European Union.
"Our arrival and my official visit is clear and direct support to Serbia to be given a date for EU accession negotiations," Pusic said, adding that getting a date would be a recognition of the big steps Serbia had made.
She said the Belgrade-Pristina agreement on normalisation of relations was important for Croatia too, as well as for the entire region, and that Zagreb expected a positive European Council decision.
Asked by the press about the possibility of Croatia and Serbia withdrawing the genocide suits they filed against each other, Pusic said attempts were being made to ensure prerequisites for the elimination of some outstanding issues and difficulties to enable serious talks on the withdrawal of the suits.
"I hope we will be able to eliminate the obstacles to the outstanding issues and that we will reach an agreement," she said.
Vucic said it was important that both countries' officials had stopped with policies that could harm the other side and recognised the need to regulate relations in the best interest of the two countries' citizens.
"We still have outstanding issues and problems but we are here to solve them and not create new ones. The lawsuits bring huge problems and costs for both states and create difficulties for future generations who don't remember our conflicts and wars. I think we will find the best solution for both Croatia and Serbia," said Vucic.
He and Pusic analysed the progress made in six areas they defined during their meeting in Zagreb, saying progress was felt in each area.
Vucic announced the publication of textbooks in Croatian for Croat minority pupils in Serbia who take classes in the Croatian language, stressing that Serbia would do everything for Croats in Serbia to feel proud as its citizens.
Pusic said both sides "have made headway and agreed the next steps in each of the six areas, from handling the pensions issue to the search for the missing (in the war)." She said Croatia would soon find a solution to the payment of pensions to people who live in Serbia but had earned their pensions in Croatia.
Asked whether Serbian President Tomislav Nikolic would attend a celebration of Croatia's EU entry in Zagreb on July 1, Pusic said, "Yes, (he) confirmed his arrival."
Vucic congratulated Pusic and Croatian citizens on the EU accession, hopeful that "Serbia and Croatia will cooperate as European partners one day as well" and that "Serbia will be able to repay Croatia for the support it has received in the European integration process."