Iraq wants a new start to improve its strained relations with Turkey and is extending an olive branch to its neighbour, Prime Minister Nuri al-Maliki said in an interview published on Thursday.

"The current situation does not satisfy anyone, neither the Iraqi nor the Turkish people," Maliki was quoted as saying by Turkey's Hurriyet newspaper in an interview conducted in Baghdad.

"We want a new start to our political relations with Turkey," he said, adding that he wanted to extend "a hand of friendship" to his Turkish counterpart Recep Tayyip Erdogan.

"Despite our differences, we would like to have a good dialogue with Turkey. I am extending an olive branch, we would like to cooperate in all areas with Turkey. But Turkey must not interfere in Iraqi internal affairs."

And Maliki once again denounced Ankara for its refusal to extradite fugitive Vice President Tareq al-Hashemi, who has been given four death sentences by a Baghdad court on charges of running a death squad.

"How would you feel if I granted asylum in Baghdad to the head of the PKK," Maliki asked, referring to the Kurdistan Workers' Party, which took up arms in Turkey's southeast in 1984 seeking autonomy for the Kurdish-majority region and which Ankara along with the US and the EU considers a terrorist group.

The fate of Iraq's fugitive vice president is one of several bones of contention that have strained the once close ties between Ankara and Baghdad.

Others issues include the Syrian conflict, the Turkish military presence in Iraq to pursue Kurdish rebels, and how to share the region's oil wealth.

On Tuesday, Iraq barred the plane of Turkey's energy minister from landing in Arbil, the capital of the autonomous Kurdistan region, who was reportedly on his way for the completion of an oil and gas development deal.

And in November, Iraq blocked Turkish national energy firm TPAO from bidding for an oil exploration contract, a decision Erdogan said was not "smart business," and accused Baghdad of acting "childishly".