By Oana Lungescu
BBC European affairs correspondent, Brussels
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The announcement comes a week after the EU signed a deal that could pave the way for Serbian membership of the bloc.
Brussels is clearly hoping that the deal and the prospect of easier travel will give Serbia's pro-European camp the edge over the nationalists.
The free visas, announced by France, are believed to benefit up to 80% of people in Serbia.
The 17 countries that have decided to issue free visas include France, Germany, Italy, Austria, but also non-EU member Norway.
Serbs have needed a visa to visit the rest of Europe since the Yugoslav wars a decade ago. So most young people who will vote in Sunday's election have never travelled abroad.
European Commission spokesman Friso Roscam-Abbing said Serbia itself had "knocked on the door to Europe".
"What we're doing now is we're opening up the doors to Europe with the various steps we've recently agreed upon, which we're now going to put to them and we are welcoming them, to become ultimately a member of the big European family."
The vice-president of the European Commission is going to Belgrade on Wednesday to start talks on eventual visa-free travel.
But that will take months if not years, as Serbia first needs to meet strict EU standards on border controls, the fight against crime and issuing biometric passports.
The nationalist parties want to bring Serbia closer to Russia after a majority of EU member states recognised the independence of Kosovo, proclaimed by its ethnic-Albanian leadership in February.
Nationalists strongly criticised last week's pre-membership accord and election posters have appeared in Belgrade depicting Serbia's pro-Western politicians as "enemies of the state".
(BBC)
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