Abbott told Modi that a warm welcome awaits him when he travels here in November this year on a bilateral visit after the G-20 Summit.
The Australian Prime Minister conveyed sympathy and solidarity over the floods in Jammu and Kashmir.
Modi told his counterpart that he had touched the heart of every Indian and the visit had resulted in concrete outcomes and new dimensions to the strategic partnership between India and Australia.
"Both the Prime Ministers agreed to actively follow up the decisions reached in the summit," a PMO statement said
During the visit, the two countries signed civil nuclear agreement under which Australia will supply uranium to the energy-starved country.
The two sides also agreed to enhance cooperation in key areas of security and trade.
The two leaders today also exchanged views on regional and international developments.