Modi later said his overnight stay at Belur Math was like "coming back home".
The Prime Minister, who had arrived at the Swami Vivekananda founded Belur Math in Howrah district on Saturday evening by launch from Kolkata and put up for the night at its international guest house, woke up early on Sunday and participated in the Mangal arati.
He then met the senior monks and prayed with them before going to the temple of Swami Vivekananda for meditation.
On May 10, 2015, Modi had prayed and meditated at the ascetic-philosopher's bedroom, on his previous visit to the monastery, around a year after becoming the Prime Minister.
Modi then went to the main temple and paid tribute to Ramakrishna Paramhamsa, before taking prasad offered by the monks.
The Prime Minister had in his youth wanted to become an ascetic of the Ramakrishna Mission, but was asked by its former president Swami Atwasthananda to concentrate on jana seva (public service) instead.
Later, addressing the youth in the monastery's premises, Modi said Swami Vivekananda's ideas were still relevant.
He said the world had lot of expectations from the youth of the country.
"If you're a youth, you deal with challenges and don't run away," he said.
Swami Vivekananda's birth anniversary is celebrated as National Youth Day.
Modi later took a launch ride to Kolkata where he inaugurated the sesquicentenary celebearions of Kolkata Port Trust.
( With inputs from IANS )