Addressing a gathering of students and teachers at the National Science Centre here, Williams told the youth to follow their dreams despite failures.
Williams said that it is important to inspire the young to take up research in science, maths and technology.
"I think that one of the key things that we do is inspire young girls and boys to research science and math and technology to follow in our footsteps of course. Some of the things we are doing also hopefully will just help in general to everybody on earth, some of the research that we are doing as well as show that women and men in any type of profession treating each other with respect and care is the right way to go, she said.
Williams lauded the Chinese space programme commending them on their efforts and progress made by them.
"Well, I will make one comment about the Chinese, we are very happy for them, and its pretty amazing the things that they have done. That they are able to launch people into space, have a space station, do a space walk, have a first woman into space so congratulations to the Tigernauts and the Chinese space program its pretty impressive so we are very excited for them," said Williams.
"I think anybody who is a space traveller is rooting for your space compatriots to be successful and to have a safe flight," she added.
Williams, who began her India trip today, will next fly to Mumbai and spend Wednesday and Thursday in the financial capital, before going to Gujarat.
In Mumbai, the astronaut is scheduled to visit a working women’s hostel managed by the Indian Council of Social Welfare in Chembur and talk to residents and students.
She will hold another interactive session with school children at the Nehru Science Centre in Worli.
Her final destination in India would be Gujarat, where she would pay a visit to her ancestral village.
Williams, who was bestowed an honorary doctorate degree by the Gujarat Technical University, will address students there.
Williams last visited India in October 2007, when she gave a talk at the Indian Institute of Technology, Mumbai.