Indonesia and Australia took the first steps at mending frayed ties as Prime Minister Malcolm Turnbull dropped in during a regional tour.

In a clear attempt at reconciliation yesterday, Australia's new leader publicly said he had offered support for Jakarta's bid to join the Trans-Pacific Partnership (TPP).

The offer was part of Mr Turnbull's efforts to reset ties with Indonesia that had soured under former prime minister Tony Abbott. Disputes over boat people, the live cattle trade, an embarrassing spying scandal as well as incursions into Indonesian waters by Australian vessels had badly hurt relations.

Prior to his arrival, however, Mr Turnbull was careful to present his trip to Jakarta as one focused on enhancing economic and security ties, rather than mending fences.

He said the prospects of working with Indonesia to grow their respective economies have never been better, and that he looked forward to a collaborative relationship with President Joko Widodo.

"We would welcome Indonesia becoming part of the TPP and if Indonesia chooses to apply... we will support its application, absolutely," said Mr Turnbull on the first stop of a 10-day overseas tour.

"The President and I had a wonderful meeting this morning and, today, he and his wife Iriana have been so warm to me and Lucy," he said. "We've talked about jobs. We've talked about infrastructure and investments and both of us believe that this is the most exciting time in the history of human development."

Mr Turnbull was speaking to reporters during a walkabout with Mr Joko in Jakarta's Tanah Abang market, after a bilateral meeting at the presidential palace. There was no sign of tension between the leaders.

Mr Turnbull is said to be the first foreign head of state invited by Mr Joko to go on one of his trademark blusukan, or impromptu visits. The positive overture was not lost on the Australians.

Mr Turnbull returned the favour by abandoning his business suit for a white shirt with no tie - another Widodo trademark. He was also heard addressing his Indonesian counterpart as "Jo" on his first visit since taking office in September.

Mr Turnbull's visit comes ahead of the Indonesia Australia Business Week 2015, and Trade Minister Andrew Robb will lead a 344-strong delegation to Jakarta on Tuesday.

"My government is absolutely committed to building on what is already a strong friendship and a strong financial-economic relationship," added Mr Turnbull.

Besides inviting Australia to invest in cattle breeding and infrastructure, Mr Joko made a pitch to Mr Turnbull on Indonesia's digital economy which, according to Ernst & Young, is now valued at US$13 billion (S$18.5 billion) and could rise to US$130 billion by 2020.

Mr Joko said they also discussed boosting cooperation in fighting radicalism and terrorism. Mr Turnbull said he was impressed with the way Indonesia has made "clear that what these extremist groups preach is not the Islam that your nation worships and your people practise".