UPDATE 2-FAA finds cracks on at least 2 AMR 767s

* FAA says could have caused engines to fall from aircraft

* AMR says it caught cracks ahead of inspection cycle

* AMR shares down 3.8 pct

* Boeing shares down 1.7 pct (Adds Boeing statement; updates shares)

CHICAGO, June 22 (Reuters) - The U.S. Federal Aviation Administration said it found structural cracks on at least two of AMR Corp's AMR.N American Airlines' fleet of Boeing 767 wide-body planes during recent safety checks.

The FAA said on Tuesday that the cracks could have caused engines to fall from aircraft.

The cracks were discovered on engine pylons on three of American's 73 767s, according to the FAA, but an AMR spokesman said the cracks appeared on only two planes.

"We are working with the carrier and the manufacturer to identify the source of the cracking and to develop remedies," an FAA spokeswoman said. "We are also considering additional action, including requiring more frequent inspections of the engine pylon area."

A Boeing Co (BA.N) spokesman said the company may issue a change to the recommended inspection interval for the part.

AMR said inspectors found the cracks while working on another part of the aircraft. The inspection that ordinarily would have found such cracks was not yet due.

"This is how maintenance is done," said AMR spokesman Tim Wagner. "We caught these when they should be caught, in fact earlier than the inspection cycle would have mandated. So that's the way you want to find them."

Shares of AMR were down 3.8 percent to $7.93 on the New York Stock Exchange in afternoon trading. Shares of Boeing were down 1.7 percent at $66.84, also on the NYSE. (Reporting by Kyle Peterson in Chicago and Sakthi Prasad in Bangalore; Editing by Derek Caney and Tim Dobbyn)