Several major airlines rolled back a weekend fare increase Monday, the first time in more than half a dozen attempts that a widespread price...

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NEW YORK — Several major airlines rolled back a weekend fare increase Monday, the first time in more than half a dozen attempts that a widespread price boost failed to take hold across the struggling industry.

Carriers wouldn’t say whether the shift signaled concerns about falling customer demand. Still, the decision served as a reminder that passengers — many reeling from money worries of their own — may be near a tipping point for how much they will pay to fly.

“This could be the first sign that demand is softening,” said Graeme Wallace, chief technology officer of airfare research site FareCompare.com. “Up until now, the [airlines’] statements have been that they expect demand to stay high.”

American Airlines launched the $20 round-trip increases Saturday. That move was quickly matched by many of its closest competitors, including United Airlines and Delta Air Lines.

Continental Airlines was among the carriers that matched the increase over the weekend, but it rolled back the higher prices Monday morning, putting pressure on rivals to do the same.

Spokeswoman Julie King said the Houston carrier rescinded the increase “for competitive reasons.”

Carriers are barred from collectively agreeing to raise or lower fares, but nothing stops them from following a rival’s lead. As a result, most major airlines tend to jockey for position when filing fares to a central booking system, which is updated three times daily.

Airlines are scrambling to cut costs and increase revenue as jet-fuel prices have soared 77 percent in the past year.

A number of airlines have laid out sweeping plans to cut jobs, slash flights and ground dozens of less efficient planes. Carriers hope they can push fares even higher by reducing the number of available seats in the air.

The industry has been generally successful in raising prices and fuel surcharges in recent months.

Twelve out of 17 increases have taken hold since the start of the year, with six of the successful increases coming in the last two months, according to a FareCompare tally.

Because the industry is so price-sensitive, carriers typically keep airfare increases in place only if rivals match the prices on the same routes. That has prompted airlines to look for other ways to boost revenue.

American, the biggest U.S. carrier, last month raised the stakes when it became the first major carrier to say it would start charging some fliers $15 to check the first bag. The airline also raised a number of other charges.

“Even when we raised fees a couple of weeks ago, we said that wasn’t the only thing we were doing, that we would still be trying to recoup fuel costs through fare increases,” spokesman Tim Wagner said. “The [fuel cost] increase is so incredible, we have to find a way to pass it on.”

American’s new baggage charge is to take effect on tickets bought on or after next Sunday. The carrier last week said the $15 fee would affect fewer than one in four customers this summer and won’t lengthen lines at boarding gates.

Other major carriers, many of which charge to check a second bag, have not said they will begin charging passengers to stow a first bag in the cargo hold, although they are not ruling it out either.

Associated Press reporter Schuyler Dixon in Dallas contributed to this story.