The country's path towards EU membership has been blocked for years, mainly due to disputes between Serbs, Bosniaks and Croats over how to enter the union.
But Biden said the US government was committed to helping Balkan nations to gain EU membership.
"The door is open for the countries of this region for the first time in history to be an integral part of a free Europe. The US will help you walk through that door," he said.
Biden, the highest-level US official to visit Bosnia since Bill Clinton in 1999, landed in Sarajevo on Tuesday to hold talks with the country's rotating three-person presidency, which represents Bosnia's Serb, Muslim and Croat populations.
But his arrival is being met with mixed feelings: Bosniaks, the nation's Muslim population, are eager to see greater US involvement, while Serbs remain wary of Washington's intentions in the region.
Biden's visit comes after the US House of Representatives adopted a resolution last week calling for urgent constitutional reforms in Bosnia.
Javier Solana, the EU foreign policy chief travelling with Biden, said the country must quell political tensions in order to join the 27-nation bloc.
"I get very sad sometimes when I see some of the nationalist rhetoric coming back," he said.
"People and the leaders together have to work in order to arrive there [the EU], the sooner the better."
Valentin Inzko, the international community's high representative in Bosnia, told Al Jazeera the country could join the EU by 2014.
|Biden will meet Bosnian Serb and Bosniak leaders during his visit to the country [EPA]
He agreed that the economic crisis could potentially exacerbate underlying tensions in Bosnia, but said it was also a time for solidarity.
"On the surface, there is this danger. But if you compare how it was to 10, 12 years ago, there was tremendous progress made."
Biden's visit sparked protests across Bosnia's Serb region on Tuesday, with hundreds of people lighting candles in a display of dissatisfaction over US plans to bolster ties with the region.
"Joe Biden arrived to tear apart Serbia and the Republika Srpska [Bosnia's Serb Republic],'' Bogdan Subotic, a former Bosnian Serb general, said.
But it is Biden's visit to Belgrade, Serbia's capital, on Wednesday that is expected to draw the most controversy.
Serbia's ties with the US worsened when Washington backed the unilateral declaration of independence last year by the province of Kosovo.
The recognition of Kosovo by most Western nations also angered Russia, Serbia's long-time ally.
During his stay in Bosnia, Biden will meet Milorad Dodik, the Bosnian Serb prime minister, and Haris Silajdzic, the Muslim member of the rotating presidency.
Ultimate political authority in Bosnia comes from the "high representative", a position established by the European Union and the US to oversee the implementation of peace deal, who can overturn laws or fire officials seen as endangering the treaty.
That position is currently held by Valentin Inzko, an Austrian diplomat, who will accompany Biden in his meetings on Tuesday.
Officials had hoped to eliminate the high representative's oversight powers several years ago.
But they have not done so amid concerns about growing Bosnian Serb assertiveness.
As a US senator during the 1992-95 war in the Balkans, Biden supported arming Bosnian Muslims in their fight against Bosnian Serbs.