But nationalist parties urged the former US senator to leave the country, holding up signs with slogans such as "Biden, you Nazi scum, go home" during a parliamentary session.
Nationalists accuse Biden of being the chief advocate of Nato's bombing of Serbia in 1999 over the Kosovo conflict, and also resent his lobbying for Bosnian Muslims in their 1992-5 fight against Bosnian Serbs.
They have opposed his visit, saying it amounts to a "humiliation'' of the country.
Washington's backing for the unilateral declaration of independence last year by the province of Kosovo also angered the Balkan nation as well as Russia, its long-time ally.
In a live televised broadcast from parliament, opposition Radical Party deputies, who occupy around a fifth of places in the assembly, appeared dressed in T-shirts bearing the image of Vojislav Seselj, the party's president, who is currently on trial for war crimes before a UN tribunal in The Hague, the Netherlands.
Dragan Todorovic, Seselj's acting leader, described Biden's visit as "the saddest day in Serbia's history".
He said the US represented "all bad things that have struck the Serbian people, and whose inspirer was, for the large part, Biden".
Several hundred Radical Party supporters also staged a protest in a Belgrade suburb, despite a police ban on demonstrations against the US planned by nationalists during Biden's visit.
Soldiers and police have lined routes during Biden's travels in Serbia, keeping the public away.
During his visit, Biden attempted to quell disagreements over the status of Kosovo.
He promised that Serbia's refusal to recognise the province's self-declared independence would not hinder its attempts to enter the European Union.
|While nationalists oppose his visit in Serbia, Kosovo looks to welcome Biden [AFP]
"We do not expect Serbia any time soon to recognise Kosovo," he said.
"But we expect Belgrade to co-operate with the European Union and other key international actors on Kosovo and look for pragmatic solutions that will improve the lives of its people, Serb and Albanian."
Tadic said Kosovo's declaration of independence violated international law, but said his country sought a partnership with Washington.
"Notwithstanding our different positions on the Kosovo question, Serbia wishes for the best possible relations with the United States, as partners," he said.
He said he and Biden had "agreed that we now have an opportunity to establish a completely new level of communication between our two countries".
Biden's visit to Serbia is part of a three-day visit to the Balkans.
During an address in Sarajevo, Bosnia's capital, on Tuesday, he pledged to support attempts by the region's nations to enter the EU and urged Bosnia's leaders to heal ethnic rifts to prevent violence from erupting in the country again.
He said: "Today, to be very blunt with you, I personally, and the leadership of my country, is worried ... about the direction of your country and your future."
Bosnia has been plagued by ethnic divisions since the US-brokered Dayton peace accords ended the country's civil war in 1995.
Biden concludes his Balkan trip with a visit to Kosovo on Thursday.