US energy giant Chevron said Thursday it had bought two exploration blocks in Iraq's autonomous Kurdish region, despite Baghdad's protests that such deals are illegal.

"Chevron Corporation announced that its subsidiaries have completed a transaction to acquire interests in two blocks in the Kurdistan region of Iraq," it said in a statement on its website.

The firm said it would acquire 80 percent stakes in the Rovi and Sarta blocks from India's Reliance.

"The blocks are located north of Arbil and cover a combined area of approximately 490 square miles (1,124 square kilometers)," the statement said.

Chevron's announcement came as Iraqi Prime Minister Nuri al-Maliki pledged to take the "necessary steps" if American energy giant ExxonMobil implemented a controversial oil exploration deal with Kurdistan.

The central government says all oil contracts must go through Baghdad and regards any that do not as illegal. It has said in recent months that the deal has been frozen, which Kurdistan has denied.

The spat is one of several between the central government in Baghdad and Kurdish authorities in Arbil.

"We remind the company of its commitments, and the need to follow the recommendations of the government," Prime Minister Nuri al-Maliki said in a statement on his website.

If ExxonMobil did not comply with Iraq's demands that it abandon its deal in Kurdistan, "the government will take the necessary steps to enforce the law and prevent the company from implementing its contracts," the statement said.