"When we empower women in the family, we empower the entire household.. when we help with women's education we ensure the entire family is educated," he said.
The Prime Minister was speaking after launching the subsidised two-wheeler scheme on the occasion of the 70th birth anniversary of late Chief Minister Jayalalithaa.
"Wherever she is, I am sure she will be very happy to see the happiness on your faces," he said as he gave away keys and registration certificates to the first five beneficiaries of the scheme.
Tamil Nadu Chief Minister K Palaniswami and his deputy O Panneerselvam, among others, were present at the launch.
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Amidst thunderous applause, the Prime Minister began his speech in Tamil, saying, "Tamil manilathirkum, mozhikum parambariyathirkum, ungalukkum, nan thalai vanangugiren," (I bow to you, the Tamil Nadu State, Tamil language, and heritage).
He also said in Tamil that he was proud to be in the soil of revolutionary poet Subramania Bharathy.
Modi addressed the late Chief Minister as "Selvi Jayalalithaa Ji," while paying tributes to her.
On women's welfare, Modi said that when one facilitates their good health, it keeps the entire family healthy and "when we secure her future,we secure the future of the entire home."
He said the Centre was also focussing on facilitating ease of living for the common citizen and that all government schemes "are oriented to cover this aim."
On NDA government's achievments in the last four years, he said it included easy credit for farmers' small business and sanctioning of over 11 crore loans under the PM Mudra Yojana worth Rs 4.60 lakh crore to people without any bank guarantee.
"The success of this scheme therefore has proved that women of India are now stepping out of the age-old shackles and seeking self-employment," Modi said.
He said the budget for the next fiscal has proposed reduction of EPF contribution for new women employees from 12 to 8 per cent while keeping the employee contribution at 12 per cent.
Under the standup India scheme, women entrepreneurs would be given loans worth between Rs 10 lakh and Rs one crore. Changes have also allowed them to work in night shifts as well.
He said that under the PM Awaz Yojana, the registration of a house is done in the name of women.
As far as Jan Dhan Yojan was concerned, it had benefited women in a big way, with them accounting for 16 crore of the total of 31 crore accounts.
Modi said the percentage of total bank accounts held by women had gone up from 28 per cent in 2014 to 40 per cent at present.
"The Swachch Bharath Mission has given women respect and dignity which is their right," he said,adding rural sanitation coverage in country has expanded from 40 per cent to 78 per cent.
So far 9.5 lakh women in Tamil Nadu have benefited from the Ujwala scheme that gives free gas connections, he said.
More than Rs 24,000 crore worth of projects are currently being implemented by the Centre in Tamil Nadu, he said, adding all these commenced after the NDA came to power.
These included solar power plants, crude oil pipleines, national highways and port related works.
Modi also said that over Rs 3,700 crore have been sanctioned for the chennai metro rail.
For urban housing, the State had been given over Rs 6000 crore, he said.
The Prime Minister said the NDA government was also working towards modernisation of fishing in Tamil Nadu.
"Under the Blue Revolution Scheme, we are providng financial aid to fishermen for long liner trawlers," he said, adding that the state government was given Rs 100 crore last year to convert over 750 boats to long liner trawlers.
Besides making their lives easier, such trawlers will also help fishermen earn more, he said.
"We remain committed towards working hard to bring a positive change in lives of people.