Territorial Health Minister Malladi Krishna Rao told reporters on Tuesday that the two patients, hailing from the neighbouring Reddiarpalayam, are a woman and her daughter.
They have been admitted to the Indira Gandhi Government Medical College Hospital which has been designated as a COVID-19 centre.
The total cases discharged so far were 12.
Rao voiced concern over the constant rise in number of active cases of pandemic over the last few days in Puducherry.
"People should be very aware of the need to adhere to the norms of lockdown although the government had intensified its steps to seal the borders in a bid to prevent flow of people from neighbouring districts of Tamil Nadu which has been registering a spike in cases," the Minister said.
On Monday, three cases were reported taking the number of infections in the union territory to 32.
With Tuesday seeing two cases, the total number has increased to 34. COR NVG NVG