ERBIL, Iraq, April 14 (Reuters) - An Iraqi central bank manager in the autonomous Kurdistan region was arrested as part of a probe into an alleged illegal bond trading scheme that may have cost the cash-strapped government more than one billion dollars.

Adham Karim, the head of the Iraqi central bank in the Kurdish regional capital Erbil, was taken into custody on Wednesday along with his deputy, a police spokesman said.

The two men are being investigated in relation to the alleged illicit trade of government-issued financial instruments, according to the head of the Kurdistan region's integrity commission Ahmed Anwar.

"This is a very big case in the Kurdistan region," Anwar told Reuters in an interview on Thursday. "It is a case involving the trading of bonds that the government had given to contractors. The investigation will reveal the details".

Anwar said the arrest of the central bank manager Karim did not necessarily mean he would be charged with a crime. Reuters could not immediately reach Karim or his office for comment. The office of the central bank governor was unable to immediately comment on the matter when contacted.

The arrests are the first high-profile action since the region's President Masoud Barzani vowed last month to fight corruption with the same determination its peshmerga forces have battled Islamic State militants.

An economic crisis induced by low oil prices has put renewed focus on corruption in Kurdistan, which enjoyed an oil-fuelled boom in the decade following the U.S.-led invasion of Iraq in 2003.

Deeply in debt, the Kurdistan Regional Government (KRG) has been implementing austerity measures and seeking financial aid abroad, but at home, people are questioning how a decade of oil riches were spent.

Ezzat Sabir, the head of the finance, economy and investment committee in the Kurdistan regional parliament estimated the government had incurred losses of more than one billion dollars from the embezzlement case about which Karim is being investigated.

(Reporting by Stephen Kalin and Isabel Coles; Editing by Toby Chopra) ((isabel.coles@thomsonreuters.com; +964 790 191 7024; Reuters Messaging: isabel.coles.reuters.com@reuters.net))