The crash involved a Russian-made Sukhoi Su-30, carrying two pilots, and a French-built Mirage 2000, operated by a third.

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

"The aircraft were on routine operational flying training mission," the country's air force said in a statement, adding that one of the three pilots had sustained fatal injuries.

An investigation was underway to determine the cause of the crash, it added.

Police officer Dharmender Gaur told AFP from the scene of the crash that another pilot had been found alive but injured in the forests of Padargarh around 300 kilometres (185 miles).

"We have located the wreckage of one of the planes," the officer said. "The other plane has likely fallen further away from the site and we have sent teams to locate it."

Local authorities had been instructed to assist with the air force's rescue and relief work, Madhya Pradesh Chief Minister Shivraj Singh Chouhan tweeted.

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

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Prime Minister Narendra Modi's government is grappling with the urgent task of overhauling India's outdated armed forces.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