He said one Pakistani aircraft was shot down, something Pakistan denied. The pilot is missing in action. "We are ascertaining the facts", said Raveesh Kumar, spokesman for Indian External Affairs Ministry.
It stepped up dramatically this week when Indian jets bombed what Delhi said was a terrorist training camp on the Pakistani side.
One of the aircraft fell into Indian-controlled territory while the other crashed onto the Pakistani side, where the pilot was captured.
Both the Indian jets were shot down by the PAF pilots.
Retired diplomat Lalit Mansingh said on Wednesday that India's policy of strategic restraint "is no longer". From us, there is a message of peace.
"I once again invite India to come to the negotiating table", he said.
Addressing his Indian counterpart Narendra Modi in a televised speech, Khan said: "Better sense should prevail".
"It is up to India now to go the way we have gone".
However, Islamabad disputed the claim, saying that while India's warplanes had entered Pakistani airspace, that they were forced to drop their bombs in an empty field after Pakistan Air Force jets were scrambled to intercept them.
Pakistan for its part also responded with air raids across the line of control (LoC) which separates Indian- from Pakistan-administered Kashmir and claims to have downed two Indian fighter jets.More news: Massive fire at Bengaluru's Aero India show, 100 cars gutted
More news: North Korea's Kim reported en route to Vietnam summit with Trump
More news: FRA pulls funds from California high speed project
Nuclear-armed India and Pakistan have fought two of their three full-fledged wars over the Himalayan territory since their partition during independence from Britain in 1947.
Update, 9:35 Eastern: India expressed outrage over Pakistan's treatment of the captured pilot, calling it a "vulgar display of injured personnel".
Earlier, in a statement, Pakistan's Foreign Ministry said that Pakistan Air Force undertook strikes across Line of Control from within Pakistani airspace.
U.S. Secretary of State Mike Pompeo spoke separately with the foreign ministers of India and Pakistan and urged them to avoid "further military activity" following Tuesday's air strike. "Sole goal being to demonstrate our right, will and capability for self defence".
It was clearly conveyed that India reserves the right to take firm and decisive action to protect its national security, sovereignty and territorial integrity against any act of aggression or cross-border terrorism.
A map of the Kashmir region.
"The Indian air force responded strongly and they were pushed back", the official said.
Tensions have been high between Islamabad and New Delhi since a February 14 suicide attack that killed at least 41 Indian troops in Muslim-majority Kashmir, which is claimed by both countries.
The statement said Indian troops "retaliated for effect" and claimed to have destroyed five Pakistani posts. In a press conference after the Indian attack, Pakistan's top military spokesperson strongly refuted the idea that it had been caught off-guard and promised India a befitting response at a time and place of its choosing.
Pakistan then conducted a retaliatory strike in which its planes locked their targeting radars on six Indian ground targets to demonstrate their capabilities but then fired their ordnance into empty spaces to avoid causing any damage or casualties.