BRUSSELS, Jan 24 (Reuters) - EU antitrust regulators on Wednesday opened an in-depth investigation into British Airways owner IAG's bid to buy the rest of Air Europa which it does not own, saying the deal may reduce competition on domestic, short-haul and long-haul routes.

IAG, which also owns Iberia, in February last year said it had agreed to pay 400 million euros ($435.9 million) to Spain's Globalia for the 80% of Air Europa it did not already own.

The European Commission said the deal may lessen competition on domestic routes to the Balearic and Canary islands.

It said the deal may also reduce competition on short-haul routes between Madrid and the main cities in Europe, Israel, Morocco, the U and Switzerland.

Another area of concern is long-haul routes between Madrid and North and South America. The EU competition enforcer set a June 7 deadline for its decision.

IAG's Chief Executive Luis Gallego reiterated the company's willingness to offer remedies to address the EU concerns.

($1 = 0.9177 euros) (Reporting by Foo Yun Chee)