The cybersecurity company said the airline should take the blame after it struggled to rebound from a software outage that caused disruptions worldwide.

The legal saber rattling between the cybersecurity company CrowdStrike and Delta Air Lines over the global I.T. outage last month just ratcheted up a notch.

In a letter sent to Delta last night that was reviewed by The New York Times, CrowdStrike’s lawyers at Quinn Emanuel Urquhart & Sullivan pushed back against claims that it was responsible for the airline’s canceling hundreds of flights. The blame for Delta’s woes lies with the airline alone, the lawyers wrote.

The letter was in response to Delta’s hiring of David Boies, a prominent litigator, and saying that it would seek damages over the outage, which it said cost it $500 million. Shares in both companies have plunged since the July 19 outage, with CrowdStrike down more than 35 percent.

In an interview with NPR, Transportation Secretary Pete Buttigieg — whose department is investigating Delta over the outage — provided preliminary observations about what went wrong: “Their systems seem to have been more dependent on pieces of software that were affected by CrowdStrike,” he said, “and we’re told also that their crew scheduling system for positioning people basically got overloaded.”

CrowdStrike questioned why Delta suffered more than its rivals. The security company cited Delta’s “I.T. decisions and response to the outage” and noted that the airline turned down “free onsite help from CrowdStrike professionals.”

Other carriers, including American and United, rebounded faster from the outage. Aviation experts told The Times that Delta leaned more heavily on cancellations than delays and had trouble getting operations back to normal.

CrowdStrike implied that its liability was limited. While Delta’s chief executive, Ed Bastian, told CNBC that the $500 million estimate factored in lost revenue and “tens of millions of dollars per day in compensation and hotels,” the software company’s lawyers countered that “any liability by CrowdStrike is contractually capped at an amount in the single-digit millions.”

CrowdStrike’s lawyers added: “Should Delta pursue this path, Delta will have to explain to the public, its shareholders and ultimately a jury why CrowdStrike took responsibility for its actions — swiftly, transparently and constructively — while Delta did not.”

Asked for a comment, a representative for Delta referred DealBook to Mr. Bastian’s CNBC interview.