Gandhi in her condolence message said, "Through his many roles in films, television ad theatre, Alter earned a special place in the hearts of Indian audiences. He leaves behind a rich legacy."
She prayed that his family, friends and admirers may find strength in this hour of grief.
Congress vice-president Rahul Gandhi also condoled Alter's death.
"Tom Alter ji's contribution to cinema & theatre is immense. Sad to know of his demise. The void left behind by him will be difficult to fill," he said in a tweet.
Alter was 67.
The Padma Shri awardee was diagnosed with skin cancer last year and was treated for the same but earlier this month he suffered a relapse and was admitted in Saifee hospital.