Prime Minister Manmohan Singh on Friday spoke to Indian-American astronaut Sunita Williams and invited her to visit him in New Delhi.
Dr Singh said Williams was a "role model" for Indian children and a "source of inspiration" for Indian women, a Prime Mminister's Office spokesman said.
Williams, who created a record of spending 195 days in space, arrived in Gujarat from London on Thursday. She is on a week-long visit to the home state of her father.
The astronaut visited the famous Sabarmati Ashram of Mahatma Gandhi on Thursday and will go to her ancestral home in Jhulasan on Friday.