He said he is "delighted by the unprecedented response" the scheme has received so far as he noted that over five crore bank accounts have been opened within five weeks of the launch against a target of 7.5 crore accounts in the first year.
"This is primarily due to your diligence and commitment. I had urged you to ensure that no one is left behind without a bank account. I always had faith in the ability of our system to rise to any challenge and with your unflinching dedication, sense of purpose and hard work, your results have far exceeded expectations," he wrote.
The Prime Minister had earlier sent an email to bank officers and staff on August 25 before launching the scheme on August 28.
"However, as we move ahead from here, the journey is bound to become more difficult and achievements harder to come by. Reaching the last few who do not have bank accounts is going to be progressively more difficult. We must not slacken our efforts in ensuring full coverage," he told the bankers.
"This is also the time to reflect and make mid-course corrections as required," he said.
The Prime Minister told the banking staff that a lot of effort will be required in promoting financial literacy amongst the new account holders and new accounts also need to be kept alive and properly utilized.
Aadhaar numbers will need to be seeded in bank accounts, facilities like e-KYC must be gainfully utilized and bank branches and 'Bank Mitras' will have to play a more proactive role so that every account holder is reached by a banking agent regularly, Modi said in the email.
"I am confident that with the kind of enthusiasm and commitment that you have demonstrated, we will succeed in achieving Pradhan Mantri Jan-Dhan Yojana's objectives as planned," he added.
Later Prime Minister Narendra Modi tweeted that over 5 crore accounts have been opened in five weeks and this was due to the hardwork and commitment shown by the bank employees.
"Response to Jan-Dhan Yojana has been unprecedented! Over 5 crore bank accounts have been opened within 5 weeks of the launch. We have to continue to reach out to those at the end of the queue & ensure they have bank accounts.
"Full coverage is the need of the hour. Hardwork & commitment of bank employees convinces me that we will succeed in achieving objectives of Jan-Dhan Yojana," the PM tweeted.