A senior Kurdish official has criticised Baghdad for keeping funds from Iraqi Kurdistan while financing areas under Islamic State (IS) control.
Iraqi Kurdistan intelligence chief Masrour Barzani told the BBC he was also concerned about Baghdad funding unofficial Shia militias.
He warned any revenge attacks by the militias in Sunni areas could create an even worse situation.
Militia and Iraqi troops are currently trying to oust IS from Tikrit.
'Must fight together'
Mr Barzani said that if the entry of Iranian-backed Shia militias into Sunni areas led to sectarian reprisals, it could exacerbate Sunni-Shia tensions.
"There shouldn't be any revenge. This is going to create a bigger problem than ISIS [Islamic State]," he said.
"We all have to look at this as a fight against ISIS. All of us have to together fight ISIS.
"But if revenge, retaliation between sects or religions, ethnic groups happens then this will become a much more difficult problem and its control is going to be even more difficult."
In Iraq's biggest offensive so far, some 20,000 militia fighters and 3,000 Iraqi soldiers are trying to oust IS from Tikrit.
However, operations were put on hold on Monday to minimise civilian and military casualties in and around the northern city, Iraqi officials said.
They said that IS fighters were now confined to an area of the city centre.
Iraq considers Tikrit's recapture as a vital stepping stone to other IS-held territory, including Mosul - the country's second largest city.
Mr Barzani was clearly furious that the Shia militias - as well as the administration in IS-held areas - were being paid by the government in Baghdad while it was withholding budget funds from Kurdistan and its Peshmerga forces battling IS, the BBC's Jim Muir in northern Iraq says.
"They [Iraq's government] are paying Mosul, they are paying Anbar [province], which are under the control of ISIS. Why aren't they paying Kurdistan, who is an ally? We are fighting a common enemy, how come we are not getting the appropriate support?"
The central government in Iraq has not been funding Kurdish areas in the north because of an oil production row.
The Popular Mobilisation militias
- Popular Mobilisation comprises dozens of Shia militias and takes a lead role in Iraqi operations against IS.
- Members have been accused of committing atrocities and acting with impunity
- The Shia-led government formed the militias in June 2014 after the army collapsed in the face of an advance by IS across northern Iraq
- Iran provides funding, weapons and military advisers to the militias and reportedly controls several of them directly
- The militias are led by Jamal Jaafar Mohammed, who is close to Iranian General Qassem Soleimani