Four men have been nabbed in this connection, the police said.
One of the accused also suffered bullet injuries in the shootout, said SSP (Meerut) Manzil Saini.
Shrikant Gaur, who practises at a hospital in east Delhi, was kidnapped on July 6 from Preet Vihar while travelling in a cab. After kidnapping him, the abductors demanded a ransom of Rs 5 crore from his family members, who informed the police.
The policemen then spoke to the kidnappers posing as representatives of the cab aggregator. They told the kidnappers that they would pay the ransom amount since it was their customer who had been kidnapped.
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On July 16, they were following a vehicle being driven by the kidnappers. However, after their vehicle got punctured, the accused left their vehicle and fled through some fields there, the police said.
The police identified two of the accused as Sushil and his brother Anuj, residents of Dadri village.
It also emerged that two others -- Ombir and Gaurav Sharma -- were involved in the kidnapping. Sushil is a driver with the cab aggregator firm and he had planned the kidnapping, the police said.
This evening the Delhi Police team received information that the doctor was being held captive at a house in Partapur village in Meerut.
The police team surrounded the place where the doctor was being held captive.
Following an exchange of fire between the Meerut and Delhi Police teams and the kidnappers, the doctor was rescued and four accused were nabbed, said the officer.
The doctor is being brought to Delhi by a police team.