The Mahan Air plane was travelling from Tehran to Guangzhou in China.
“IAF fighter aircraft were scrambled, which followed the aircraft at a safe distance,” the air force said.
“The aircraft was offered the option to land at Jaipur and then at Chandigarh,” it said, referring to airports in the west and north of the country.
The pilot declined to land at either airport. The bomb threat turned out to be a false alarm.
“After a while, intimation was received from Tehran to disregard the bomb scare, following which the aircraft continued on its journey towards its final destination,” the air force said.
Demonstrations have continued despite the use of force against protesters by security forces. Almost 100 people have been killed in the past three weeks.
Fire officials told to stand down
Officials at Delhi’s fire and emergency services said they received information about the bomb threat at 9.30am and alerted staff.
But airport authorities later asked them to stand down after the flight proceeded towards its destination, Sanjay Tomar, a senior official at the services, told a local news outlet.
Several flight tracker websites showed the aircraft's path leaving Tehran and crossing into the Indian airspace early on Monday, after flying over Pakistan.
It made several mid-air loops around an area west of Delhi before heading east towards China.
Indian authorities have not confirmed the flight number involved in the bomb scare.
Recent bomb hoaxes
Indian authorities have dealt with similar hoaxes in recent days.
The country’s largest private airline IndiGo issued an alert at the weekend and had a plane checked after receiving an email claiming an explosive was on board a flight from Mumbai to Ahmedabad.
After a thorough search of the plane, the threat was found to have been a hoax.
On Sunday, a Malaysia-bound flight was grounded at Indira Gandhi International Airport in Delhi after staff raised a bomb alert following an argument between two passengers over an overhead luggage cabin, with one falsely claiming he had an explosive device in his bag.