Friday is the second day of his India visit.
Syed Akbaruddin, external affairs ministry spokesperson, in a tweet said Abbott thanked India for a "splendid ceremonial welcome", as he met the minister.
There was a formal welcome ceremony by Prime Minister Narendra Modi who expressed his confidence of strengthening relations with Australia. "A warm welcome to PM Tony Abbott! I am sure his visit will further strengthen ties between Australia and India," Modi said in a tweet.
The welcome ceremony left the Australian prime minister impressed. Abbott tweeted: "A spectacular official welcome to India by prime minister."
Abbott also visited Rajghat - memorial to Mahatma Gandhi on the bank of Yamuna river.
He was received at the airport by Piyush Goyal, union minister of state (independent charge) for power, coal and new renewable energy. "India-Australia set to re-energise ties," Akbaruddin tweeted earlier.
Abott arrived in Mumbai on Thursday.