Iraq's army must do more to protect a northern oil pipeline and should pay as much attention to it as it does to fighting militants, Iraq's top energy official told AFP Sunday.

The rare criticism of the security forces comes with the pipeline, which connects the northern province of Kirkuk to the Turkish Mediterranean port of Ceyhan, having been disabled for three months as a result of militant attacks as the army grapples with a year-long nationwide surge in violence.

"I have pointed out repeatedly that this -- protection of the export pipeline -- should be a national priority, no less than confronting the terrorists in Fallujah or elsewhere," Hussein al-Shahristani, deputy prime minister responsible for energy affairs, said in an interview.

He was referring to battles between security forces and anti-government fighters who have held sway over Fallujah, a city a short drive west of Baghdad, since the beginning of the year.

"I believe the army should have taken more action to protect these pipelines than they have done so far," Shahristani said, speaking from his office in Baghdad's heavily-fortified Green Zone.

He said the army was expected to have had a new specialised division dedicated to protecting the Kirkuk-Ceyhan pipeline up and running by the end of March, but the required arms and equipment had yet to arrive.

"Unless the army can provide sufficient protection along with the oil police, the chances are that the pipeline could be attacked," Shahristani said.

The pipeline, which at its peak in 2011 was pumping upwards of 500,000 barrels of oil per day (bpd), has been disabled since early March and while repairs are currently being carried out, it is not expected to be functional for several more days.

Shahristani's remarks came as Iraq announced that oil exports had increased for a second month running to 2.58 million bpd, all shipped from the country's southern export terminals.

His comments mark a rare criticism of the Iraqi army, which has been grappling with a year-long surge in bloodshed that has left more than 4,000 people dead already this year, according to an AFP tally.

In particular, Iraq's security forces have struggled to wrest back control of Fallujah, which has been out of government control for months.

The crisis in the desert province of Anbar, which borders Syria and of which Fallujah is a part, began in late December when security forces dismantled a longstanding protest camp maintained by the province's mainly Sunni Arab population to vent grievances against the government.

Militants subsequently seized parts of the provincial capital Ramadi and all of Fallujah, the first time anti-government forces have exercised such open control in major cities since the peak of the deadly violence that followed the 2003 US-led invasion of Iraq.

They have held all of Fallujah since, and protracted battles have continued for Ramadi.