TOKYO, July 12 (Reuters) - Japanese airline ANA Holdings canceled 330 domestic flights from July 23 through July 31, and warned of further cancellations in August as it continues to inspect engines built by Rolls-Royce.

The airline said on Monday it had canceled 176 flights from July 13 through July 22 to inspect Trent 1000 engines.

Britain's Rolls-Royce has been hit by a problem with a compressor in the Trent 1000 package C engine, grounding planes, forcing inspections and angering airline clients.

ANA said cancellations in August would likely be fewer per day than in July. (Reporting by Maki Shiraki; Editing by Muralikumar Anantharaman)