The Dadasaheb Phalke Awardee, 81, has been facing the ire following his support towards authors returning their Sahitya Akademi awards in protest of the growing religious intolerance in the country.
"Gulzar Saab's love for this country, its people and his conscience is far beyond the collective vitriol of the lynch mob that attacks him," Anurag posted on Twitter.
The "Gangs of Wasseypur" director and Gulzar have worked together in "No Smoking" and "Satya".
Many writers have returned their Akademi awards to protest the killing of Kannada writer M M Kalburgi and other growing instances of attacks on intellectuals.
Gulzar had said while the killing was not Akademi's fault, the authors wanted the institution to recognise and protest against the incident.