"All primary contacts and secondary contacts of both the cases have been traced and are being tested," the health ministry's joint secretary Lav Agarwal told a news briefing.
India was set to restart scheduled commercial international flights on Dec 15, but on Wednesday scrapped that plan and said a resumption date would be announced in due course.
The government has advised states to ramp up testing, a week after the health ministry said a recent fall in testing could undermine India's efforts to contain the pandemic.
After battling a record jump in infections and deaths in April and May, coronavirus cases have come down substantially in India, where the delta variant is the dominant strain.
The country reported 9,765 new cases on Thursday, taking its total to 34.61 million. Only the United States has reported more.