In an address to the nation, Pakistan's prime minister Imran Khan said he was ready to sit down and talk with India in order to avoid any "miscalculations" following air strikes by both sides.
He added that he hoped "better sense" would prevail to de-escalate tensions with its nuclear-armed neighbour.
"History tells us that wars are full of miscalculation. My question is that given the weapons we have can we afford miscalculation," he said during a brief televised address.
He said Pakistan would cooperate with India in an investigation concerning the suicide car bombing by Pakistan-based militants in Indian-controlled Kashmir that killed at least 40 Indian paramilitary police on February 14.
Tensions between the two nuclear-armed countries have been running high since the suicide bombing but the risk of conflict rose dramatically on Tuesday when India launched an air strike on what it said was a militant training base.
The attack targeted the Jaish-e-Mohammed (JeM), the group that claimed credit for the suicide attack. But while India said a large number of JeM fighters had been killed, Pakistani officials said the Indian airstrike was a failure and inflicted no casualties.
Earlier on Wednesday, Pakistan said it shot down two Indian jets after its neighbour yesterday conducted a cross border airstrike for the first time since a war in 1971.
Indian air force planes strayed into Pakistani airspace on the same day after Pakistan had carried out airstrikes in Indian-occupied Kashmir, said Major General Asif Ghafoor, a spokesman for the Pakistan armed forces.
"PAF shot down two Indian aircraft inside Pakistani airspace," he said in a tweet.
One of the aircraft fell on India's side of Kashmir, while the second came down in Pakistani-held territory, and its pilot was captured, he added.
In another statement, Pakistan's foreign ministry said it had struck "non military targets" but avoided "human loss and collateral damage".
A spokesman for India's foreign ministry said it lost a combat jet and could not find the pilot while it foiled an attack by Pakistan military planes in Kashmir.
"In this engagement, we have unfortunately lost one MiG 21. The pilot is missing in action. Pakistan has claimed that he is in their custody. We are ascertaining the facts," Raveesh Kumar told reporters.
Pakistan has not said anything about losing one of its planes.
This is the first time in history that two nuclear powers launch air strikes at each other.
Both countries claim the entire mountainous Himalayan region of Kashmir but rule in part.
Indian officials said three Pakistani jets had also entered Indian airspace, before being intercepted and forced to turn back.
The Indian air force ordered Kashmir's main airport in Srinagar and three other airports to close down because of the incidents.
Pakistan shut down its airspace in light of the current situation.
In a separate incident, police officials in the Indian part of Kashmir said that two Indian pilots and a civilian had died after an Indian aircraft crashed in the region. The craft initially reported to be a plane appears to be a Mi17 military helicopter according to a partial tail number seen by Reuters.
The cause of the crash is still unknown.
US 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.
"I expressed to both ministers that we encourage India and Pakistan to exercise restraint, and avoid escalation at any cost," Pompeo said in a statement on Wednesday.
"I also encouraged both ministers to prioritise direct communication and avoid further military activity," he said.