Both aircraft had taken off in the morning from the Gwailor air base, around 50 kilometres (30 miles) east of where they came down.

"We have located the wreckage of one of the planes and found an injured pilot in the Pahadgarh forests," officer Dharmender Gaur told AFP from the scene of the crash.

"The other plane has likely fallen further away from the site and we have sent teams to locate it."

The air force was investigating whether the planes had collided in mid-air, local broadsheet the Hindustan Times reported.

The Su-30 was carrying two pilots and the Mirage jet had one on takeoff, according to the report.

"I have instructed the local administration to cooperate with the air force in quick rescue and relief work," Madhya Pradesh Chief Minister Shivraj Singh Chouhan tweeted.

"I pray to god that the pilots of the planes are safe."

The crash is the latest in a string of aviation accidents involving India's military air fleet.

Five army soldiers were killed last October when their helicopter crashed in Arunachal Pradesh state, near the country's militarised and disputed border with China.

It was the second military chopper crash in the state that month, coming weeks after a Cheetah helicopter came down near the town of Tawang, killing its pilot.

India's defence chief, General Bipin Rawat, was among 13 people killed when his Russian-made Mi-17 helicopter crashed while transporting him to an air force base in December 2021.

Prime Minister Narendra Modi's government is grappling with the urgent task of overhauling India's outdated armed forces.

Its military establishment is fretting over a growing assertiveness by China along its vast Himalayan frontier, which in 2019 sparked a lingering diplomatic freeze after a deadly high-altitude confrontation between troops of both countries.

India unveiled its first locally built aircraft carrier last year as part of government efforts to build an indigenous defence industry and reduce reliance on Russia, historically its most important arms supplier.

An effort to reform military recruitment to trim down India's bloated defence payroll stalled last year after a backlash from aspiring soldiers, who burned train carriages and clashed with police in fierce protests.