Visiting Prime Minister Narendra Modi, speaking at a joint news conference with French President Francois Hollande, said India wants the aircraft to be "ready to fly," meaning the planes would be made in France. That is a departure from an earlier plan for 126 Rafales mainly built in India.
"France has always kept in mind our requirements, our critical requirements, and this is why I, once again, asked the president to provide us with 36 Rafales that are ready to fly," Modi said, "and this in the near future."
"We also decided that the terms and conditions would be modified on this particular question," he added.
Hollande said India wanted the deal sealed "in the shortest time possible."
Egypt signed a deal for 24 Rafales in February, the first overseas buyer of France's delta-winged, multi-role, but hard to sell jet fighters, made by Dassault Aviation. Rafales have been on the market for years, and in service for the French Air Force since 2006. They are currently being used by France in the international coalition's strikes on Iraq against the Islamic State group.
Talks between France and India for the sale of Rafales began three years ago.
French Defence Minister Jean-Yves Le Drian, speaking to The Associated Press, said future talks would involve a possible transfer of technology and manufacture of Rafales in India, believed to be one of the country's main requests.
No price tag was put on the eventual deal. However, the sale to Egypt of 24 aircraft was valued at 5.2 billion euros ($5.93 billion), a French Defence Ministry official said at the time. The initial Indian deal, for 126 Rafales, was priced at 12 billion euros ($15 billion).
India has become the world's biggest arms importer, with an economic boom enabling it to modernize its military. Major arms manufacturers are wooing the country as it replaces its obsolete Soviet-era weapons and buys new equipment. India already has a fleet of the older Mirage jets, France's last big-name fighters.
India's air force has around 700 fighter aircraft and is exceeded in size only by the United States, Russia and China.
Competing jets from the United States and Russia, such as the General Dynamics F-16, McDonnell Douglas F-15 and Sukhoi Su-27, have grabbed a large slice of the market.
The Indian deal with France appeared all but clinched. It was preceded by back-and-forth talks. Le Drian travelled to India in December. A decision was then made to accelerate negotiations, a ministry official said. New Delhi then voiced its need for operational aircraft, which would be planes made in France and ready to go.
The French and Indian leaders signed a series of contracts in energy, transport and space exploration, and the Indian prime minister said there had been "a great deal of progress" on construction of six EPR nuclear reactors.
Modi will travel to Germany and Canada after his two-day visit to France ends Saturday.