PARIS (Reuters) - French oil major Total (>> TOTAL), which rattled Baghdad two years ago by signing a deal with Kurdistan, says it is too early to predict whether the semi-autonomous Iraqi region may turn into an important oil player.

As violence threatens the unity of Iraq, there are predictions that Kurdistan will seek independence and quickly aim to become a major oil producer.

The regional government hopes output could jump five-fold in the next few years to 1 million barrels per day and is seeking greater autonomy from Baghdad, which insists only the central government has the right to sell Kurdish oil.

Arbil is betting multiple deals with Western companies to explore its reserves will put it firmly on the map among the fastest growing producers, but majors such as Total are more cautious.

"If Kurdistan were a huge petroleum region, we wouldn't have waited until 2010," Total chief executive Christophe de Margerie told Reuters in an interview.

"It is too early to make a judgement. You can't yet see what we call a production curve... You have to avoid underestimating or overestimating the potential."

Total bought stakes in two exploration blocks in Kurdistan in 2012 from U.S. peer Marathon Oil (>> Marathon Oil Corporation), drawing an angry response from the Iraqi government which has tried to bar companies from dealing directly with Arbil.

Elsewhere in Iraq, Total has a relatively modest exposure as partner at the south-eastern Halfaya field. France's opposition to the U.S.-led 2003 invasion of Iraq did not endear French companies to the new authorities.

Most oil majors cite unattractive terms of Iraqi contracts as being behind their decisions to explore more lucrative Kurdish deals.

"Why hasn't Kurdistan got the right to develop its reserves? I've defended that and it has cost me a couple of problems with Baghdad," said De Margerie.

But he also suggested Kurdistan was unlikely to eclipse Iraq on the global oil map: "Kurdistan isn't Baghdad - one shouldn't make this mistake."

He also said companies could not remain indifferent to security risks such as violence in Syria even if Kurdistan looked stable compared to some other regions of Iraq.

"There is escalation in Syria. Every time you want to simplify things because it suits you, those things refuse to be simplified," De Margerie said.

(Writing by Dmitry Zhdannikov; Editing by Paul Taylor and David Evans)

Stocks treated in this article : TOTAL, Marathon Oil Corporation