Yana Peel, who has overseen the two Serpentine galleries for three years, said the criticism was based on "inaccurate media reports now subject to legal complaints."
A private equity firm co-founded by Peel's husband Stephen, Novalpina, is majority stakeholder in NSO Group, maker of Pegasus software.
Pegasus allows for monitoring of devices and their content, including the remote activation of cameras and microphones without users' knowledge.
The firm says the software is used by authorities to help prevent terrorist attacks, infiltrate organized crime groups and help rescue kidnapped children.
Human rights campaigners say Pegasus has been used by authoritarian regimes to spy on citizens.
NSO said last week that it was setting up a "governance framework" to ensure its software was used lawfully.
Peel, a longtime free-speech advocate, claimed that "bullying and intimidation" might lead wealthy donors to stop funding arts institutions.
"I welcome debate and discussion about the realities of life in the digital age ... but they should be constructive, fair and factual - not based upon toxic personal attacks," she said.
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