Joe Biden and Boris Tadic spoke of "mutual respect"
US Vice-President Joe Biden has assured Serbia that the two countries can open a new page in relations, regardless of differences over Kosovo.
Mr Biden is the highest-ranked American to visit Serbia since the US led a Nato bombing campaign to expel Serb forces from Kosovo in 1999.
He said the US backed Serbia's plans to join the European Union.
Serbian President Boris Tadic said the two states could progress "on the basis of dialogue rooted in mutual respect".
But he made clear that Serbia would not give ground over its claims to Kosovo, which declared independence last year.
"Serbia does not recognise Kosovo's independence, and would never recognise it. Serbia has the legitimate right to defend its territorial integrity peacefully by diplomatic and legal means," he said.
Mr Biden said: "The United States does not, I emphasise, does not expect Serbia to recognise the independence of Kosovo.
"It is not a precondition for our relationship or our support for Serbia becoming part of the European Union," he said.
The US and most EU countries have recognised Kosovo's independence, but a majority of countries have not.
A Serbian opposition party is running an anti-Nato exhibition during the visit
Mr Biden is on a tour of the Balkans. On Tuesday he visited Bosnia and on Thursday will go to Kosovo itself.
The rare visit by a top US official marks a new effort by the Obama presidency to re-engage with the Balkans, BBC Eastern Europe correspondent Nick Thorpe reports.
But the US remains deeply unpopular among some Serbs.
Belgrade, where protesters torched the US Embassy in February 2008, banned all public gatherings on Wednesday.
MPs from the hardline nationalist Serbian Radical Party held up banners in parliament saying: "Biden, you Nazi scum, go home."
Another opposition party put on an exhibition of harrowing photos, showing civilian victims of Nato air attacks in 1999.
In Bosnia on Tuesday, Mr Biden urged MPs in the multi-ethnic federal parliament to seize the opportunity they had been offered to integrate their country into the EU.
Otherwise, he said, Bosnia would remain among the poorest countries in the region and might even slip back into ethnic chaos.
Criticising nationalist politics, he said: "God, when will you tire of that rhetoric?"
"This must stop," he added. "Let me be clear: Your only real path to a secure and prosperous future is to join Europe. Right now, you're off that path."
Washington has traditionally supported a united Bosnia and played a central role in ending the war in the mid-1990s in which more than 100,000 people died.
The Dayton peace treaty cemented the division of the country into two republics with only weak federal structures.
Efforts since then, and constitutional reform, have been largely thwarted by Bosnian Serb governments afraid of losing Serb power in their half of the country, our correspondent says.
But the EU insists that central institutions be strengthened before Bosnia can be considered for membership.