"I utterly reject all allegations of impropriety," he added.
The controversy erupted last week when HP recorded a $9 billion asset impairment charge, a big chunk of it, or about $5 billion, related to Autonomy.
The company said the British software firm was "substantially overvalued at the time of its acquisition due to the misstatement of Autonomy's financial performance, including its revenue, core growth rate and gross margins, and the misrepresentation of its business mix."
Lynch joined HP after the merger, but was ousted earlier this year. In his letter, he contended that HP's accusations simply didn't make sense, saying, "Many observers are stunned by HP's claim that these allegations account for a $5 billion write-down and fail to understand how HP reaches that number. Please publish the calculations used to determine the $5 billion impairment charge."
Responding to Lynch's letter, HP in a statement maintained that it has "uncovered extensive evidence of a willful effort on behalf of certain former Autonomy employees to inflate the underlying financial metrics of the company in order to mislead investors and potential buyers."
But the company said the case is "in the hands of the authorities, including Britain's Serious Fraud Office, the U.S. Securities and Exchange Commission's Enforcement Division and the U.S. Department of Justice."
"We will defer to them as to how they wish to engage with Lynch," the company said. "While Lynch is eager for a debate, we believe the legal process is the correct method in which to bring out the facts and take action on behalf of our shareholders."
HP's write-down sent the stock plunging last week. The stock, which closed down 3 percent Tuesday, at $12.36, has shed more than 50 percent of its value year-to-date.