The pilot was injured and was being treated at a military hospital, Ghafoor said. He did not elaborate on the pilot's injuries.
Ghafoor struck a conciliatory tone. "One of the aircraft fell inside AJ&K [Pakistan-controlled Kashmir] while other fell inside IOK [Indian-controlled Kashmir]".
Witnesses said soldiers fired in the air to keep residents away from the crash site.
Pakistan's civil aviation authority said it shut Pakistani airspace to all commercial flights on Wednesday, without elaborating or indicating when flights might resume.
Pakistan has shot down Indian fighter jet in a response to Indian aggression a day earlier.
Hussain reported from Srinagar, India.
I'm a flying pilot of the Indian air force (IAF), he continued in his statement.
Pulwama attack and Indian election drama resulted into loss of 2 Indian Jets shot down by Pakistan Air Force.
"We encourage India and Pakistan to exercise restraint, and avoid escalation at any cost", Pompeo said in a statement after speaking with his counterparts from both countries.
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Indian early warning aircraft and aerostat radars are on full operational alert to look out for Pakistani aerial activity.
Other media in the region have claimed the plane was shot down by Pakistan.
Post the IAF strike, the Pakistan army warned India saying "It is your turn now to wait and get ready for our surprise". The chopper split into two, and caught fire.
The Himalayan region has been divided between India and Pakistan since independence in 1947.
Kashmir is split between sections under Indian and Pakistani control.
Local officials on the Pakistani side said at least four people had been killed and seven wounded, though it was unclear if the casualties were civilian or military.
The confrontation represents the first major foreign policy crisis for Pakistani Prime Minister Imran Khan, who is believed to be close to the powerful military and who came to power a year ago vowing to seek dialogue with New Delhi.
India's external affairs minister, Sushma Swaraj, said Wednesday her country does not wish to see further escalation of the situation with Pakistan and that it will continue to act with responsibility and restraint.
India's action came after Pakistani F-16 jets allegedly violated Indian airspace in retaliation for Indian Air Force jets bombing a Jaish-e-Mohammed terror camp in Khyber Pakhtunkhwa on Tuesday.
Tensions have been elevated since a suicide vehicle bombing by Pakistan-based militants in Indian-controlled Kashmir killed at least 40 Indian paramilitary police on February 14, but the risk of conflict rose dramatically after India's air strike on Tuesday.