The premier, considered a hardline nationalist, swept to power last month on a pledge to reform the economy and boost manufacturing and local production.
"Why should we import defence equipment? We must be self sufficient," Modi's office tweeted him as saying while on board the carrier off the coast of Goa.
"Why can't we send our defence equipment to other nation?" he said.
"We need to give immense importance to latest technology. This will help the nation," he added.
Russia handed over the 44,500-tonne INS Vikramaditya carrier to India late last year after a refit that overran by five years and went vastly over budget, damaging ties between the countries.
Russia is India's largest arms supplier.India last August unveiled a domestically produced carrier, and the INS Vikramaditya is its second, intended to shore up the country's defence capabilities as it seeks to counter a military build-up by an increasingly assertive China.
"Security of the country is our top priority," Modi was also quoted by the Press Trust of India news agency saying.
"We want to see eye to eye with the world. We don't wish to threaten others, neither do we wish to bow down before others."
The new carrier is 284 metres long and is designed to carry 30 aircraft.
The induction comes after a fully-armed submarine exploded in flames and sank last year in a military shipyard in Mumbai, killing 18 sailors.
Six months later, a submarine accident off the Mumbai coast left two sailors dead.