Addressing a function on the occasion of 'Hindi Divas' in New Delhi, the President said Hindi continued to face opposition in some parts of the country even though it became an official language many decades ago.
Home Minister Rajnath Singh, who was also present at the function organised by his ministry, said in his address that Hindi could be enriched further if its speakers also used words from other languages.
Referring to recent incidents on the Bangalore Metro, where a pro-Kannada group opposed Hindi signboards in the train service, and earlier agitations against Hindi in Tamil Nadu, President Kovind said there was a feeling among some people that Hindi was being imposed on them.
"Non-Hindi speaking people desire that we (Hindi-speaking people) give attention to their languages. Those who speak Hindi should give space to other languages. We all have the responsibility to give respect to non-Hindi speaking people and regional languages," he said.
President Kovind suggested that those who speak Hindi should greet a Tamilian with a 'vanakkam', a Sikh with 'Sat Sri Akal' and a Muslim with an 'Adaab' -- words of greeting in Tamil, among Sikhs and in Urdu respectively. They should use the word 'Garu' (sir) while addressing a Telugu-speaking person, he said.
The adoption of other languages and cultures will help unite the people and the country, he said.
The president said he had used the Russian word 'spasiba' (thank you) while ending his speech at a state banquet during the recent visit of Belarus President AG Lukashenko. The guest was so delighted that he spontaneously responded with a 'Jai Hind'.
The Belarus president also announced that Hindi would be taught in their state university from this month.
President Kovind also asked lawyers and doctors to use Hindi and other regional languages at work.
"In India people don't understand the language of lawyers and doctors. In courts, now, gradually Hindi and other languages are being spoken. Similarly, if the doctors start giving prescriptions in Devanagari and other languages, the doctor-patient distance will be reduced," he said.
In his address, the home minister said Hindi was the unifying language for the country and had helped bring people of different regions together during India's freedom struggle.
"We (Hindi-speaking people) should accept and use popular words of regional languages. If we do that, it will enrich the language," he said.
Mr Singh said the contribution of non-Hindi speaking people such as Mahatma Gandhi and Bal Gangadhar Tilak was immense in making Hindi an official language of the country.
He also questioned those who said English was required for India to become an economic power. "I want to ask those who say that without English India can't be an economic power, how come China has become an economic power by speaking Mandarin," he said.
In his welcome speech, Union minister of state for home Kiren Rijiju said even though Hindi was not his mother tongue, he felt immense pride while speaking the language.
"In my native state (Arunachal Pradesh), Hindi is widely spoken and used by common people from all walks of life," he said.
All the speakers spoke in Hindi at the function. Hindi is the mother tongue of the president and the Union home minister.