The airline is looking at 250,000 people or more who will be bumped from their flights, reports CBS News correspondent Nancy Cordes.
A spokesman said the cancellations would go into Saturday, but that American expected all of the grounded planes to be flying again by Saturday night.
Cordes reports that as of Thursday evening, American hadn't even reached the halfway mark with their inspections.
Of the 300 MD-80s in its fleet, it's inspected and fixed the wiring harnesses in just 130.
Other carriers operating similar aircraft also left passengers scrambling for alternatives as they also grounded flights to inspect the wire bundles at the heart of a renewed safety crackdown by the Federal Aviation Administration.
Alaska Airlines canceled 11 more flights early Thursday as it continued to inspect its nine MD-80 jets. Spokeswoman Caroline Boren in Seattle said that follows 28 cancellations on Wednesday and three on Tuesday. The airline was working to accommodate affected passengers, she said.
Midwest Airlines canceled at least 10 flights Thursday after it grounded all of its 13 MD-80 planes to deal with the same issue. Spokesman Mike Brophy said federal regulators cleared the planes to fly, but airline executives decided they should be re-inspected by Midwest personnel.
Delta Air Lines was likely to ground "a handful of flights" Thursday, but was expecting "minimal cancellations and minimal customer impact," spokeswoman Betsy Talton said. The carrier operates 117 MD-80 series planes.
The problems could be just beginning. The latest checks are part of a second phase of audits being carried out by the FAA, which came under pressure from lawmakers after its inspectors were found to be too lax with Southwest Airlines Co. last year. That round of inspections runs through June 30.
American, the nation's largest carrier, said Friday it had canceled 933 flights for the day. The airline has now scrubbed nearly 2,500 flights since Tuesday, when federal regulators warned that nearly half its planes could violate a safety regulation designed to prevent fires. That's more than one in three flights canceled over the last three days.
American estimates that more than 100 passengers would have been on each of those canceled flights. That means a quarter-million people have been inconvenienced this week.
Tim Wagner, a spokesman for American, said the cancellations would extend into Saturday, but said it was too soon to know how many flights would be dropped Friday or Saturday.
A return to normal operations depends on how quickly mechanics can inspect and fix the wire bundles.
Wagner said as of mid-morning, the FAA had cleared 101 of American's 300 MD-80s to fly and 16 more were awaiting final FAA inspection. Friday's schedule assumed that only 60 of those planes would be ready, but the airline expected 180 to be flying by Friday night and the rest by Saturday night.
The fallout could be seen at airport ticket counters, where frustrated customers bickered with American employees, and on the stock market, where shares of American's parent company tumbled more than 11 percent Wednesday.
Airline executives said they thought they had fixed the wiring two weeks ago, when they canceled more than 400 flights to inspect and in some cases fix the shielding around the wires in their MD-80s.
But this week, Federal Aviation Administration inspectors, who have been conducting stepped-up surveys of compliance with safety rules called airworthiness directives, said 15 of 19 American jets they examined flunked. That left the airline no choice but to ground all 300 of its MD-80s, the most common jet in its 655-plane fleet.
"We have obviously failed to complete the airworthiness directive to the precise standards that the FAA requires, and I take full responsibility for that," said Gerard Arpey, American's chairman and chief executive.
American's executive vice president Daniel Garton apologized for the snafu and vowed that the airline would fix the problem this time.
"We simply cannot put our customers through this again," he said.
Garton added that for American, "this certainly couldn't have come at a worse time." The Fort Worth-based airline faces record fuel prices and fear of a recession, and analysts forecast that its parent, AMR Corp., lost more than $300 million in the first three months of the year.
American declined to say how much it would spend on $500 travel vouchers and hotel rooms for stranded travelers and overtime for mechanics, or how much revenue it would lose by putting some displaced customers on other airlines. But Garton said it would be "significant."
Perhaps worried about that cost, investors on Wednesday sent AMR shares down $1.15 to $9.17 - though they regained some of that Thursday, rising 6.3 percent back to $9.75.
The issue stems from an FAA order in 2006 covering the bundling of wires in the backup power system for the fuel pump of the MD-80. The FAA says improperly bundled wires could rub, leading to an electrical short or even fire.
American officials said the safety of their planes was never jeopardized, and the FAA said no serious incidents have been blamed on poorly bundled wires.