The airline canceled 595 flights Friday, 933 Thursday, 1,094 Wednesday and 460 Tuesday.
Saturday will be the fifth straight day of large-scale cancellations.
American Airlines on Saturday received clearance from federal aviation officials to return all but three of the remaining 300 grounded jets to service, an airline spokesman said.
But it won't be until Sunday morning before the MD-80s can be positioned throughout the American system to fly a full day's schedule, spokesman Charley Wilson said.
American planned to return to normal operations Saturday afternoon, Wilson said.
The nation's largest airline canceled nearly 3,300 flights. The cancellations started Tuesday as Fort Worth-based American grounded 300 MD-80 jets to wrap wiring bundles to meet federal safety standards and prevent fires.
The cancellations stranded hundreds of thousands of people during the week.
The airline's mechanics and Federal Aviation Administration inspectors cleared more of the planes to return to service Friday. American said 226 of its MD-80s were back in service by Friday morning, and it expected the rest by Saturday night.
The groundings had come as a surprise.
American officials said they thought they had the needed repair work completed two weeks ago when it scrubbed more than 400 flights, but the FAA said the wiring still was not secured and stowed properly in wheel wells.
Gerard Arpey, chairman and chief executive of American parent AMR Corp., said the costs of the cancellations to American will run into the tens of millions of dollars - including vouchers to reimburse stranded customers, overtime for maintenance crews and lost revenue. An analyst with Standard & Poor's estimated it could easily top $30 million.
Arpey said that neither American's mechanics nor the FAA were to blame for the groundings, and he said he took responsibility for the cancellations. He said the company would hire a consultant to help it comply with FAA safety rules in the future.
American's entire fleet averages 15 years in age, the second oldest in the industry behind Northwest Airlines, according to regulatory filings by the airlines.
Arpey said Thursday that American may accelerate the replacement of its MD-80s, but only because newer planes get better mileage, an important consideration with fuel at record prices. The CEO pointedly said the recent groundings were not a factor in the decision to replace MD-80s.
