Cybersecurity software company CrowdStrike is disputing Delta Air Lines over who is to blame for damage that the airline suffered after a global technology outage.

Delta's CEO has threatened to sue CrowdStrike for what he said was $500 million in lost revenue and extra costs related to thousands of canceled flights.

A lawyer for CrowdStrike says, however, that the company's liability should be less than $10 million.

Michael Carlinsky said in a letter Sunday to Delta lawyer David Boies that the airline's threatened lawsuit "has contributed to a misleading narrative that CrowdStrike is responsible for Delta's IT decisions and response to the outage."

The CrowdStrike lawyer questioned why other airlines recovered from the outage much more quickly. He said the software company took responsibility for its actions "while Delta did not."

A faulty software update from CrowdStrike to more than 8 million computers using Microsoft Windows disrupted airlines, banks, retailers and other businesses on July 19.

Delta CEO Ed Bastian raised the threat of a lawsuit last week on CNBC. He said Delta was more dependent on Microsoft Windows than other airlines. The Atlanta-based airline hired Boies' law firm to handle the matter.

Bastian said CrowdStrike did not offer to help Delta beyond offering free consulting advice. CrowdStrike said its CEO, George Kurtz, personally contacted Bastian to offer help, but got no response.

The U.S. Department of Transportation is investigating why Delta took longer to recover than other airlines. Transportation Secretary Pete Buttigieg said his department would also look into complaints about Delta's customer service, including long waits for help and reports that unaccompanied minors were stranded at airports.