His statement comes against the backdrop of controversy relating to film 'Padmavati' and cases of vigilantism.
Addressing the people on his monthly 'Mann ki Baat' programme, he said "It is our duty that we abide by our Constitution in letter and spirit.
"Citizens and administrators alike must move ahead in accordance with the spirit of our Constitution. The message that our Constitution conveys is that no one should be harmed in any way."
Some groups have claimed that the Bollywood movie shows queen Padmavati in bad light and have threatened to physically harm actor Deepika Padukone and torch theatres screening it.
There have also been fresh incidents of vigilantes attacking men transporting cows.
In his address, the Prime Minister made no reference to the incidents and the controversy.
He said the Constitution of India is the spirit of India's democracy.
In 1949, on this day, the Constituent Assembly had approved the document which was adopted the next year on January 26.
He said the members of the Constituent Assembly worked hard for about three years to draft the Constitution.
"Can you imagine how hard their task would have been to frame the Constitution of our country which has such big diversities?...Now, this is the responsibility of all of us to make a new India in the light of the thinking of the makers of our Constitution.
"Equality for all and sensitivity towards all is the unique characteristic of our Constitution. It guarantees fundamental rights to each and every citizen...it protects their fundamental rights and safeguards their interests. It is our duty that we abide by our Constitution in letter and spirit. Citizens and administrators alike must move ahead in accordance with the spirit of our Constitution. The message that our Constitution conveys is that no one should be harmed in any way," he said.
Modi also recalled the contributions of B R Ambedkar and Vallabha Bhai Patel in shaping early India.
In his address, the 38th so far, the Prime Minister also hailed the role of differently-abled (divyang) people in various fields including the drive against open defecation and sports.
"We get to learn something or the other every moment.
They are performing well in every walk of life. Whether it be the field of sports, any kind of competition or a social initiative, our divyang brethren are second to none...let the confluence of collective and the individual foster a sense of harmony in our society; let us move forward with each other, together," he said.