The leaders also discussed the recent visit of Iraqi Prime Minister Nuri al-Maliki to Washington.

According to a White House statement, the leaders discussed the current political climate in Baghdad, and the vice president "reiterated the United States' longstanding support for an inclusive partnership government in Iraq" and for a long-term strategic partnership between the United States and Iraq.

The White House did not say who initiated the call.

"Biden and Barzani also reaffirmed the longstanding friendship between the American and Kurdish people and discussed the vice president's recent visit to Turkey," the statement said.

US forces formally marked the end of their mission in Iraq with a low-key ceremony near Baghdad on Thursday.

The "casing of the colors" near the airport, the first site the US occupied in Baghdad in 2003, came with around 4,000 US soldiers still in Iraq, all of whom will depart in the coming days.

After that, all that will remain are 157 soldiers under the authority of the American embassy in Iraq, a country where there were once nearly 170,000 troops on more than 500 bases.

The withdrawal ended a war that left tens of thousands of Iraqis and nearly 4,500 American soldiers dead, many more wounded, and 1.75 million Iraqis displaced, after the US-led invasion unleashed brutal sectarian fighting.