People for the Ethical Treatment of Animals says McCartney sent a letter to Indian Prime Minister Manmohan Singh saying such a day could save animals while helping to protect both the environment and people's health.
McCartney's letter says "it would be a celebration of life."
The U.N. food agency in 2003 estimated 42 percent of India's 1.2 billion people are vegetarian, due mostly to financial and religious concerns. Strict Hindus and Jains do not eat meat.
Singh's office could not immediately confirm receipt of McCartney's letter Tuesday.