The accusation by Shiite Prime Minister Nuri al-Maliki represented another blow to American hopes that religious and ethnic factions in the country will form a united government to challenge marauding Sunni radicals.
The White House said Biden and Barzani agreed on the need to "accelerate the government formation process pursuant to the time-lines set forth in the Iraqi constitution."
A parliamentary session last week to pick a new government ended in disarray as lawmakers traded threats and walked out.
Biden also expressed condolences for the loss of Iraqis in fighting with Islamic State (IS) extremists who have captured large swaths of the country.
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Biden's office did not immediately respond when asked whether the vice president's call came as a result of Maliki's fiery comments earlier today attacking the Kurds.
The vice president has long served as President Barack Obama's pointman on Iraq -- dating back to the days when there were thousands of US troops in the country.
The US readout also did not dwell on Barzani's previous call for an independence referendum for Iraqi Kurds, a step the White House has said it would not support.
Maliki potentially complicated his efforts to form a government encompassing Kurds, Shia and Sunnis by accusing Kurdish leaders in the northern city of Arbil of hosting militant groups.
"Honestly, we cannot be silent over this and we cannot be silent over Arbil being a headquarters for Daash, and the Baath, and Al-Qaeda and terrorist operations," Maliki said on television.