Most of the Pakistani aircraft were downed by India's Russian-made S-400 surface-to-air missile system, Indian Air Chief Marshal A.P. Singh said at an event in the southern city of Bengaluru on Saturday.
He cited electronic tracking data as confirmation of the strikes.
"We have at least five fighters confirmed killed, and one large aircraft," he said, adding the large aircraft, which could be a surveillance plane, was shot down at a distance of 300 km.
"This is actually the largest ever recorded surface-to-air kill," he said, prompting applause from the crowd that included serving air force officers, veterans, and government and industry officials.
Pakistan's military did not immediately respond to a request for comment.
Singh did not mention the type of fighter jets that were downed, but said that airstrikes also hit an additional surveillance plane and "a few F16" fighters that were parked in hangars at two air bases in southeastern Pakistan.
Islamabad, whose air force primarily operates Chinese-made jets and US F-16s, has previously denied India downed any Pakistani aircraft during the May 7-10 fighting between the nuclear-armed neighbours.
Pakistan has claimed it shot down six Indian aircraft during the clashes, including a French-made Rafale fighter. India has acknowledged some losses but denied losing six aircraft.
France's air chief, General Jerome Bellanger, has previously said he has seen evidence of the loss of three Indian fighters, including a Rafale.
The Indian Air Force has not commented on the claims.
