Turnbull later met Maharashtra Governor Ch Vidyasagar Rao and left for Australia from Mumbai airport in the afternoon, a state government official said.
The duo rode the train from Mandi House station to Akshardham station.
The Australian PM also emphasised on the need to conclude the Regional Comprehensive Economic Partnership (RCEP) led by China in the wake of the U.S. rejecting the TransPacific Partnership agreement.
Earlier yesterday, both the Prime Minister hosted a joint press conference, where PM Modi had praised the Australian PM saying that his visit gave both the countries to shape new priorities in the strategic partnerships between India and Australia.
"Prime Minister Modi is leading this most remarkable nation on an extraordinary journey of growth and development". Mr Modi said that Mr Turnbull and he recognised that their future was deeply tied to peace and stability in the Indo-Pacific.
India and Australia on Monday signed six MoUs in different fields including combating terrorism, civil aviation security, and satellite navigation.
Australian Prime Minister Minister Malcolm Turnbull arrived here on Sunday on a four-day state visit to India.
"Now we are working with India to secure timely conclusion of a quality Regional Comprehensive Economic Partnership, the RCEP, which would provide a significant boost to regional confidence". As for defence ties, the two countries agreed that their ties are solid as they recalled the Special Forces Bilateral Exercise which took place in October.
They also held talks on Canberra supplying uranium to Indian nuclear power plants.
"My first visit to India as prime minister is a chance to further co-operate across a wide range of sectors including energy, education and trade", Mr Turnbull said.
Philip Hammond, the UK's Chancellor of the Exchequer, had also organised a trade delegation to India during the annual UK-India Economic and Financial Dialogue on April 2.
On his part, Turnbull said Australia was helping India in its water management policy while sharing expertise in the area of renewable energy.
This will be the first visit of Turnbull to India.