The two patients, one from Delhi and Telangana each, are stable and are being closely monitored.
Two new cases of the novel coronavirus were confirmed in India on March 2.
One case each was reported from New Delhi and the state of Telangana.
Both patients are stable and are being closely monitored, news agency ANI has reported.
The person from Delhi had travelled to Italy, the Union Health Ministry said adding that he is being treated at the RML hospital in the national capital.
The other person with coronavirus infection has a travel history to Dubai, the ministry added.
According to news agency PTI, the person in Delhi had self-reported at the RML hospital while the one in Telangana had initially gone to a private hospital and then was referred to a government hospital in the state.
The virus, now known as COVID-19, has infected over 89,000 people globally and caused more than 3,000 deaths.
As many as 25,738 people are under community surveillance across the country, Union Health Minister Harsh Vardhan said as he advised people to avoid non-essential travel to Iran, Italy, South Korea and Singapore.
The minister further said the Indian government is in discussion with Iran and Italian authorities to evacuate Indians there.
Vardhan said that so far 3,217 samples have been tested out of which five tested positive for COVID-19 while reports of 23 are awaited. Italy is reeling under swelling cases of the coronavirus disease.
Three days ago, Kerala's Health Minister, KK Shailaja had announced that three students who had earlier tested positive for coronavirus, have now been cured."We succeeded in the first part, that of containing coronavirus. Three students who were found to be corona-positive were isolated, now they are stable. They were cured," Shailaja had said.
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