Delta Air Lines Inc. is suing Republic Airways Holdings Inc., claiming that the regional airline company failed to fly some Delta Connection flights.

Republic has said it curtailed flying for regional affiliates of Delta, American and United because of a pilot shortage that it has blamed partly on a labor dispute with pilots.

Delta sued Republic in a state court in Atlanta on Monday. In the heavily blacked-out version available to the public, Delta said that it suffered “millions” in lost profits because Republic couldn’t operate all the flights it promised, causing Delta to cancel flights and scramble to find replacement planes.

In a news release on Wednesday, Republic said it was not violating any of its contracts, including those with Delta.

Indianapolis-based Republic owns Republic Airlines and Shuttle America, which together operate about 1,250 flights a day. They are part of a group of regional airlines that use smaller planes to operate flights for Delta, American and United between secondary airports and big hub airports. Regional carriers operate about half the nation’s passenger flights, although the planes prominently display the names of the big airlines that hire them.

Shares of Republic were down 42 cents, or 6.7 percent, to $5.86 in afternoon trading while shares of most airlines, including Delta, were up.

Photo Credit: A Republic Airways plane on the tarmac. Cliff / Flickr