In the account, the PMO has posted several pictures including those of the prominent visitors greeting the new Prime Minister.
Apart from the pictures, the Prime Minister's message on the occasion of 'World No Tobacco day' is in the page.
It has got thousands of 'likes', besdies hundreds of comments and suggestions. While one of Facebook users in his comments in response to the PM's message requests that prices of tobacco products be increased by levying high taxes to reduce consumption, another person suggests that consumption of tobacco products should be banned in public places.
PM Narendra Modi is an avid user of the social media.
Scores of other comments by different users express a range of opinion.
"The official Facebook page of the Prime Minister's Office has crossed a million likes in 4 days of being launched," the PMO said on Twitter.
The PMO's twitter account also has nearly 1.4 million followers.
Modi has been actively utilising the social media to connect with people and expects his ministerial colleagues to do the same.
In a recent letter to other ministries, Information and Broadcasting Minister Prakash Javadekar has said that the "Prime Minister expects all his ministerial collegues to use the social media platform extensively to disseminate new initiatives of the government."