On India's skill development programme, Turnbull said Australia's industry-led vocational education and training system can play a key role training 400 million Indians by 2022.
It will be Australian PM Turnbull's first visit to the country after assuming office in 2015.
Mr Turnbull's time in New Delhi is attracting all the trappings of an official state visit, including a ceremonial welcome at the presidential palace, wreath-laying at Gandhi's memorial and a state banquet.
With energy security an ever-present issue, India is looking for assurances from Australia that the colossal and highly controversial coal mine can proceed.
Modi nicely drew cricket analogies to describe the ties between the two countries.
"Both leaders recognised the importance of freedom of navigation and overflight, unimpeded lawful commerce, as well as resolving maritime disputes by peaceful means, in accordance with worldwide law, including UNCLOS (United Nations Convention on the Law of the Sea)", said the joint statement.
The bilateral discussion also hinted at a growing agreement to oppose China's territorial claims over the South China Sea region.
He is scheduled to hold delegation-level talks with Prime Minister Modi later in the day. They welcomed the significant progress achieved through the bilateral Framework for Security Cooperation agreed in 2014.
He also urged PNG to diversify its commodities-based economy, focusing on science and technological innovation and he offered Australia's support in this area.
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Australia's education exports to India are worth $2.3 billion a year with more than 60,000 Indian students studying in Australia last year.
He also thanked Turnbull for Australia's decision to join the International Solar Alliance.
He spoke to the media in a joint press conference with PNG Prime Minister Peter O'Neill to discuss economic ties and the future of Manus Island.
In his statement, PM Modi emphasised on peace and stability in the Indo-Pacific region, saying challenges like terrorism and cyber security require global strategy and solutions.
On his part, Turnbull appealed to universities and research institutes of both countries to focus on addressing critical problems.
"Our commitment is to assure that when jobs can be done by Australians they should be done by Australians."
Speaking on the India-Australia relationship, Mazumdar said that the relationship between the two countries was more robust and multi-faceted today than it had ever been before.
"Our strong and vibrant strategic partnership is of course important for the security and well-being of our societies".
"Alongside China, India is a land of vast opportunity for Australia", the Australian leader said.