In his greetings, Mukherjee said the last year was an important period filled with significant achievements for the Prime Minister and the country.
"This special day comes as you complete more than fifteen months as the Prime Minister of our great nation. The last year has been an important period filled with significant achievements for you personally and our country.
"Your hard work, dynamism and out of the box thinking has received wide appreciation in the country and abroad," the President was quoted by his official spokesman Venu Rajamony as saying.
Congress vice president Rahul Gandhi, with whom Modi has been engaged in bitter exchanges over a host of issues including the land bill, too extended his greetings.
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"Best wishes to Prime Minister Narendra Modiji on his birthday," Rahul tweeted.
Starting the exchange of greetings between the two, the Prime Minister had on June 19 taken to twitter to greet Rahul on his birthday.
"Wishing the Congress Vice President, Shri Rahul Gandhi a Happy Birthday. I pray for his good health & long life. @OfficeOfRG," the PM had said on Twitter as Rahul turned 45.
Congress MP Shashi Tharoor, who had to face the party's wrath for praising Narendra Modi and was dropped from the list of spokespersons, also greeted the Prime Minister but underlined their disagreement in politics.
"Happy Birthday @narendramodi . May you continue to serve India w/energy &commitment. Will continue to disagree w/ yr politics, but w/respect!," Tharoor said.
"Greetings to Prime Minister Sh Narendra Modi ji on his birthday. My prayers for his health and long life," Delhi Chief Minister Arvind Kejriwal tweeted.
"Happy birthday @narendramodi ji. May God grant you a long life in the service of the nation. #HappyBdayPM," tweeted National Conference leader and former Jammu and Kashmir chief minister Omar Abdullah.