Calls for the two UK acts to cancel their concerts emerged after Mr Ozkan went on social media to condemn a fight that broke out in a coffee shop boycotted by protesters.
"Plain and simple, this is hostility towards the capital. Act of treason," he said on X.
He later posted another message, explaining his comments were not aimed at the "constitutional right to protests", and that he "deeply regrets" any misunderstanding.
Since 19 March, police have detained nearly 2,000 people, many of them university students.
The controversy over the concerts coincides with wider calls for a countrywide boycott in Turkey which has been criticised by the government as economic sabotage.
The social media accounts of Muse and Robbie Williams have been flooded with comments calling for their concerts to be cancelled.
"You've played a huge role in shaping my musical taste," wrote one post, "but unfortunately the company organising it is on our boycott list."
Singer Gaye Su Akyol, a popular artist in Turkey, took to X to make a personal appeal to Muse, Robbie Williams and Norwegian singer Ane Brun.
"I've respected your works for years and know how much you mean to many," she said. "But neither I, nor anyone, will attend your Istanbul concerts because the organiser is on the boycott list of the pro-democracy movement. Solidarity matters."
