Abbott, Kerry hold talks in Jakarta

US Secretary of State John Kerry has passed on the president's "strong greetings" to Australia for its willingness to join coalition airstrikes on jihadist targets in Iraq.

Prime Minister Tony Abbott met Mr Kerry following the inauguration of Joko Widodo in Jakarta on Monday.

Before their talks, Mr Kerry passed on President Barack Obama's thanks, and belief the US "couldn't have a stronger partner" than Australia.

"I bring you President Obama's strong greetings and the great gratitude of him and all Americans for Australia's major stepping up in respect of coalition efforts," he said.

"We're very, very grateful for Australia's consistent willingness to step up and stand for the values as well as interests that are important to us.

"I do want to say that your efforts with respect to foreign fighters, which regrettably you have to experience at the local level, brings home to everyone how important this is to be a global effort, and for all of us to understand the stakes."

Mr Abbott said he hoped the practice of Australian leaders attending Indonesian inaugurations - and regular talks with US leaders - was now firm.

"I hope the tradition has now been established of Australian prime ministers attending the inauguration of Indonesian presidents," he said.

Mr Kerry said he also looked forward to speaking with the prime minister about Iran, Afghanistan and the South China Sea, among other issues.