The Jakarta terror attacks will be front of mind for Prime Minister Malcolm Turnbull when he sits down with the US president to discuss global security and the Islamic State threat.

The prime minister is set to receive the bells-and-whistles treatment - including residency at the prestigious Blair House - when he arrives in Washington DC on Monday (US time) for his first official visit.

Terrorism, trade and the economy will dominate Mr Turnbull's two-day agenda in the US.

Fresh from a whirlwind weekend trip to Iraq and Afghanistan, Mr Turnbull is likely to draw on his own first-hand insights into the military efforts to defeat Islamic extremists during talks with President Barack Obama and Defense Secretary Ash Carter.

In Iraq, Mr Turnbull met with Australian soldiers training local forces as well as Prime Minister Haider al-Abadi.

He emphasised the most important boots on the ground in the fight against the Islamic State group, or Daesh, had to be Iraqi.

Australia did not intend to be in Iraq forever and any further military commitment would depend on the circumstances, Mr Turnbull said.

Canberra has formally rejected what Mr Turnbull described as a "form letter" US request for increased military contributions from its coalition partners.

Australia has 780 defence personnel deployed in the Middle East providing training and conducting air strikes over Iraq and Syria.

The US-led coalition's efforts appear to be paying off with IS-held territory shrinking by about 40 per cent from its maximum expansion in Iraq in 2015.

Mr Turnbull on Sunday met with Afghanistan President Ashraf Ghani and the country's chief executive officer Abdullah Abdullah.

The prime minister received top-level briefings about the NATO-led train-advise-and-assist mission Resolute Support, which replaced the previous International Security Assistance Force mission.

Mr Turnbull spoke with a number of the 250 Australian defence personnel involved in Afghanistan during his visit.

Radical extremism closer to home in Southeast Asia will also frame Mr Turnbull and Mr Obama's discussions.

IS has taken responsibility for a series of deadly bomb blasts and gunfire which jolted the Indonesian capital last week.

The events in Jakarta have some personal significance for Mr Obama who lived there for several years as a child with his mother and Indonesian stepfather.

Mr Turnbull will also meet senior economic figures including Federal Reserve chair Janet Yellen and congressional leaders.

The controversial Trans-Pacific Partnership regional deal, North Korea, China's role as a growing power and territorial tensions in the South China Sea are among other issues expected to be canvassed during high-level talks.

The TPP is a hot-button issue in a US election year and the chances of congress approving it before the presidential poll in November are low.

Innovation is also expected to be ballyhooed during a meeting of the two leaders.

The federal government announced a $1 billion innovation package in December while Mr Obama, in his farewell State of the Union address last week, reflected on disruption to traditional industries and called for a new "moonshot" - a cure for cancer.

AAP