This is double the 18 Rafales India had originally planned to buy as part of the stalled deal for 126 aircraft that Dassault has been in talks with the Indian Ministry of Defence (MoD) about since January 2012.
The remaining 108 Rafales were to be licence-built by India's state-owned Hindustan Aeronautics Limited (HAL) for the Indian Air Force (IAF) to meet its long-delayed Medium Multi-Role Combat Aircraft (MMRCA) requirement.
"Keeping in view the critical operational necessity of fighter aircraft in India, I have asked President [Francois] Hollande to provide 36 Rafale jets in flyaway condition as quickly as possible under a government-to-government deal," Modi said at a joint press conference with the French president.
"We have decided that these will be provided to India [under] modified terms [and] conditions," Modi said following one-on-one talks with Hollande on the first day of his official trip to France.
He was drawing a distinction between the purported terms of the contract for the 36 Rafales to be acquired off-the-shelf and the under-negotiation tender for 126 fighters.
Details of the proposed Rafale procurement, Modi added, would soon be finalised by officials from both sides, but declined to elaborate.
Hollande is scheduled to chair a meeting of government officials and Dassault executives at the Élysée Palace on 13 April to work out details of the sale.
He said French defence minister Jean-Yves Le Drian would shortly travel to India to advance the fighter deal, which industry officials estimate to be worth USD5-7 billion.
Senior IAF officers said the 36 Rafales would comprise two squadrons of 14 single-seat and two twin-seat trainers each. The remaining four single-seat fighters would be part of the "maintenance reserve", a two-star IAF officer said.
An official Indian statement declared that the Rafale fighters "would be compatible to the IAF's operational requirements".
The aircraft and associated systems and weapons would be delivered on the same configuration, as had been tested and approved by the IAF and with a longer maintenance responsibility by France, it added.
Indian defence minister Manohar Parrikar, who welcomed Modi's surprise announcement, said on 11 April that Rafale deliveries would begin within two years. "It is a much-needed decision taken by Prime Minister Modi on better terms and conditions [than the one for 126 aircraft]," he told the Press Trust of India news agency.
The Rafale acquisition was operational 'oxygen' for the IAF, which has not bought a new-generation aircraft for 17 years, he added.
"The Rafale deal is a course correction and will help alleviate the frustration that has crept into French political and defence manufacturing circles about doing business with India," former Indian foreign secretary Kanwal Sibal said. It delivered a tangible result in the key area of defence co-operation, he added.
Defence sources said the decision was arrived at by a handful of officials from the Indian Prime Minister's Office negotiating with their French counterparts and Dassault representatives right up until Modi's arrival in Paris on 9 April.
The IAF also welcomed Modi's announcement, declaring that the Rafale induction would supplement its depleting fighter strength, which has dropped to 32 squadrons from 39 and is well below the government-sanctioned 42 squadrons.
But senior officers were sceptical about inducting only 36 Rafales, as their acquisition would present the IAF with logistic, doctrinal, maintenance, and even operational hurdles.
"The IAF currently operates seven different fighter types and storing spares and building maintenance facilities for just two Rafale squadrons would be disproportionate to their operational employment," a three-star officer said.
Modi's announcement, however, is silent on plans to locally build 108 Rafales under his new government's 'Make in India' campaign that is aimed at reducing dependence on imported materiel.
Defence officials interpret the prime minister's announcement - that the direct purchase of 36 Rafales via the IGA was "part of a separate process" - to mean that talks on the deal for 126 Rafales would continue.
If so, they anticipate Rafale numbers rising to 144 or even 162 aircraft, a number that needs further MoD clarification.
A Dassault Rafale multirole fighter aircraft of the French Air Force airstrike at Islamic militants group "Ansar Dine" in Mali. Equipped with optoelectronic container Thales Damocles and 2,000-liter fuel tank hanging on ventral hardpoints, two 500-pound (227-kilogram) guided bombs GBU-49 Enhanced Paveway and two drop tanks under the wings, as well as two URVV MICA-IR on endings.