Australian Prime Minister Kevin Rudd on Friday promised a "new phase of cooperation" with Indonesia on disaster response and the environment during his first state visit to Jakarta.

Rudd praised the "very strong friendship" between the two neighbours after he met President Susilo Bambang Yudhoyono and senior ministers at the presidential palace.

"Australia and Indonesia are neighbours through geographic circumstance but we are friends through active national choice, and this is a very good friendship," he told reporters after the talks.

He said the countries had agreed to broaden cooperation over nuclear weapons proliferation, climate change and disaster response.

The recent natural catastrophes in Myanmar, which was devastated by a cyclone in May, and quake-hit China underscored the need for a regional disaster response mechanism, he said.

"Indonesia has experienced the tsunami, the people of Burma (Myanmar) the terrible impact of the cyclone, the people of western China the earthquake most recently," he said.

"We do not know where a natural disaster will hit but between us we believe we can take a good and strong proposal" for a regional disaster-response system to the Asia-Pacific Economic Cooperation meeting next year, Rudd said.

The two leaders also discussed Rudd's plans for an EU-style Asia-Pacific Community to be set up by 2020 and to include the major economies of India, China, India and the United States.

He said the Association of Southeast Asian Nations (ASEAN) had provided a model of regional cooperation which could be expanded.

It was Rudd's first state visit to Indonesia since he defeated conservative prime minister John Howard in elections in November.

He flew into Jakarta late Thursday on the second leg of an Asian trip which started in Japan on the weekend. He will travel to Sumatra's Aceh province on Saturday to visit areas devastated by the 2004 tsunami.

Rudd and Yudhoyono signed an agreement on forests and carbon trading at the end of the meeting, reflecting the growing importance of climate change to the neighbours' relations.

The prime minister, who ratified the Kyoto treaty in one of his first acts after taking power from conservative premier John Howard in November, called climate change the "great economic, environmental and moral challenge of our generation".

Rudd lauded cooperation between Australia and Indonesia in fighting Islamic terror groups but refused to give a timeframe of when Australia might lift a travel warning against visiting parts of Indonesia.

"Indonesia and our future security cooperation will go from strength to strength as we continue in our common resolve to deal with our common enemy, which is terrorism," he said.

Scores of Australians were killed in terror bombings on the holiday island of Bali in 2002 and 2005, and the Australian embassy in Jakarta was attacked in 2004 as Canberra backed the US-led wars in Iraq and Afghanistan.

Ties between Indonesia and Australia are regularly tested by suspicion on both sides, reaching a nadir in 1999 when Australian troops landed in Timor Leste to help restore order after the province voted to break away from Indonesia.

Current sore points include the treatment of Indonesian fishermen suspected of illegal fishing in Australian waters and the pending execution of Australian drug traffickers jailed in Indonesia.

Rudd's moves to withdraw troops from Iraq and ratify Kyoto treaty have won broad favour in Indonesia after the more openly pro-US policies of Howard.