CHICAGO, July 27 (Reuters) - American Airlines' pilots union on Thursday said it has reached an agreement in principle with the company on enhancements to a new labor contract that would bring it in line with the gains for aviators at rival United Airlines.

The union had asked for improvements to the tentative contract agreement, saying its ratification was in "jeopardy" after United raised the benchmark with its own deal. It later put off a vote on the deal.

North American pilots have been commanding higher salaries and improved working conditions with travel demand remaining buoyant, despite airlines raising fares to cover higher costs.

The Allied Pilots Association (APA), which represents over 15,000 American Airlines pilots, did not specify the value of the revised deal. But American Airlines CEO Robert Isom last week said bringing the proposed four-year contract in line with United's deal would enhance its value by more than $1 billion, making it worth well over $9 billion.

Its revised contract includes a provision that will allow an adjustment in pay rates for pilots to match wages of their counterparts at United and Delta Air Lines, which had set the new U.S. industry standard with a deal ratified in March.

The American Airlines revised deal also provides pilots full back pay for this year.

In line with United's deal, pay increases for American Airlines' pilots will now take place on January 1 instead of May 2 as provided in the original deal.

The APA said the revised agreement needs an approval from its board, after which it would be sent for a ratification vote. A union spokesperson said the board would meet on Aug. 2-3 to review the deal.

An American Airlines spokesperson described the revised deal as a contract that its pilots deserve.

Jefferies analysts estimate the United States is short about 10,000 pilots, with the supply-demand gap projected to last until 2027.

While the APA reached a tentative deal with American Airlines in May, the union argued its proposed pay rates as well as some quality-of-life items in the agreement paled in comparison with those in United's preliminary deal.

For example, the APA pressed for additional sick days to meet gains secured at Delta and United.

Airline unions negotiate their contracts in a pattern bargaining process, where a deal at one carrier acts as a benchmark for other companies.

Southwest Airlines is now the only major U.S. carrier that is without a new pilot contract deal. (Reporting by Rajesh Kumar Singh; Editing by Leslie Adler, Bill Berkrot and Jamie Freed)