In a press statement, PM Modi said: "The waters of the Indian Ocean remind us of our linked histories".
The two leaders waved to the crowd gathered at the busy metro station, before boarding the train bound for Noida City Centre.
On a state visit to India, Mr Turnbull said he and Indian Prime Minister Narendra Modi spoke about the Comprehensive Economic Cooperation Agreement (CECA) between the two countries, but progress had not been as fast as either of them would like it to be.
The two leaders held comprehensive discussions on bilateral, regional and worldwide issues of mutual interest and concern.
India and Australia on Monday made a decision to kick-start the stalled negotiations on the Comprehensive Economic Cooperation Agreement (CECA) by holding the next round of talks soon.
The Prime Minister congratulated Modi on the creation of the International Solar Alliance, adding he was "very happy to announce that we will join that alliance".
Stronger defence key to Palace revival - Allardyce
The Palace for Life Foundation has launched with a mission to transform the lives of young south Londoners through sport, encouraging them to be more active, helping them become employable and intervening to help the most disadvantaged.
"We are aware that in this globalised world challenges like terrorism and cyber-security extend beyond boundaries of our regions", Prime Minister Modi added.
India's Prime Minister Narendra Modi (R) gesutres as his Australian counterpar Malcolm Turnbull watches during Turnbull's ceremonial reception at the forecourt of India's Rashtrapati Bhavan presidential palace in New Delhi, India, April 10, 2017. While Turnbull promised to provide more educational opportunities to Indian students, Modi praised the Australian prime minister for visiting India and giving it a chance to "shape new priorities in a strategic partnership". He also said Australia supports India's entry into the other nuclear export clubs like the Australia Group and the Wassenaar Arrangement. "We are heading to the Akshardham Temple", Modi tweeted with the selfie.
This is Turnbull's first visit to India since he assumed office in 2015.
India has collaborated with the Australian government, universities and vocational education trainers following a two-day mission that has delivered key advancements on educational issues. The two sides also failed to conclude negotiations for Comprehensive Economic Cooperation Agreement (CECA).
The two leaders also agreed to deepen cooperation in defence and security as well as in education.