In a letter to Chief Minister Jayalalithaa, he said the primary concern at this stage was to ensure the integrity of ongoing efforts for Father Prem Kumar's release and "to ensure that he does not come to harm".
"I can assure you that the Government will spare no effort for the safe and earliest possible release of Father Prem Kumar. I will continue to monitor the situation very closely", Modi said.
Modi's letter was in response to the one sent to him by Jayalalithaa on June 4, requesting him to "personally intervene" and take up the matter at the highest level in Afganistan for the early release of Prem Kumar.
Noting that he too was "deeply concerned" about the abduction of Prem Kumar, Modi said, "I have been assured that the Government of Afghanistan and the authorities in Herat are taking every possible step to ensure the early release of Prem Kumar".
Indian Ambassador in Kabul (Amar Sinha) has been in "regular" touch with the President's office and the security agencies, Modi said.
"My National Security Advisor (Ajith Doval) has also spoken to the Afghan National Security Advisor,who has assured full and sustained efforts by the Afghan Government to seek Prem Kumar's release", he said.
Indian aid worker Alexis Prem Kumar, hailing from Tamil Nadu, was abducted on June 2 from Herat in Afghanistan by unidentified gunmen, days after the Indian consulate in the province was attacked.
The Indian National was working with an educational charity in Afghanistan.