The leader of Iraq's autonomous Kurdish region insisted Friday that the United States should arm his forces fighting the Islamic State group directly instead of passing though the federal government in Baghdad.

At the end of a week-long visit to Washington to lobby for support, Kurdish leader Massud Barzani thanked President Barack Obama's administration for its support but reiterated his demand that weapons be shipped directly to his troops.

Barzani said the central government had not honored a deal struck in 2007 between US, Iraqi and Kurdish commanders that Kurdistan's peshmerga militia receive its share of US military aid from Baghdad.

"We eventually ended up having the peshmerga not receiving a bullet or a piece of weaponry from Baghdad," he told reporters.

Barzani was careful not to criticize Obama or US Vice President Joe Biden, who both met him during his visit, but pointedly thanked "our friends in Congress" who have proposed a bill that would oblige Washington to arm the Kurds.

"We have not backed down from our position, we insist that the weapons get into the hands of the peshmerga," he said.

On Wednesday, foreign policy hawks in the US Congress introduced a bill that would give the administration authority for three years to bypass Baghdad and send weapons to Arbil.

Senator Lindsey Graham, who co-sponsored the bill, described Barzani's peshmerga as "our most reliable military partner within Iraq."

The Kurdish region and its battle-hardened guerrillas have long been a US ally in Iraq, having fought Saddam Hussein's former regime and now finding themselves on the front line in the battle against the Islamic State group.

But Washington has been careful not to put Iraqi unity at risk by taking steps that would encourage the Kurdistan Regional Government to pursue its quest for eventual independence more aggressively.

The Kurdish peshmerga have been helping Iraqi government forces counter the new threat posed by the IS jihadists, but in doing so they have been operating deeper in disputed mixed Arab and Kurd areas beyond the official KRG border.

Barzani said Kurdistan would hold a referendum on self-determination "possibly this year or the next year" but that the battle against the Islamic State was its immediate priority.

"We are in a continued day-to-day fight with the terrorists, therefore practically speaking we cannot conduct the referendum right now. Our top priority is defeating ISIS, but that doesn't mean we'll wait for ever," he said.

He said there could be no question of the peshmerga leaving the city of Kirkuk, which the central government does not recognize as Kurdish territory, but that they would work with Baghdad to retake Mosul from IS forces.