Mr Turnbull's itinerary included a visit to a quantum computing start-up in Washington DC and a keynote economic speech at a chamber of commerce. Prime Minister Malcolm Turnbull delivers a speech to the Centre for Strategic and International Studies in Washington, DC. Credit:Alex Ellinghausen Mr Turnbull used his key speech in Washington, DC, on Monday to reject the notion that the world order that has been underpinned by American strength was fraying. He said the greatest period of prosperity and peace on earth – including China's rise – was due to post World War II stability that had been forged by the United States. "Some claim that the range of new global threats we see today are symptoms of receding American will, or power, and that we are watching the fraying of the post-war order," he told a packed audience at the Centre for Strategic and International studies, a leading think tank based in Washington, DC.

"We reject those pessimists. America is stronger than ever, its economy has rebounded from the Great Recession. Its military is the mightiest in the world. Its entrepreneurs and engineers have literally imagined the modern digital world." Mr Turnbull lays a wreath at the tomb of the Unknowns at Arlington War Cemetery in Virginia. Credit:Nathan Edwards He said the deep friendship between Australia and the US was not only built upon shared combat but shared values. But he said it was almost inevitable that China would return to its pre-19th century position as the dominant global economy. To avoid what he called the "Thucydides Trap" – the inevitable conflict born from the unease at the rise of a new power, China's rise must be welcomed by the world, but China must also work to reassure its neighbours that its intentions are good.

"You know as well as we do that justice is to be found only as between equals in power. As for the rest, the strong do as they will and the weak suffer as they must," said the Prime Minister, quoting from Book 1 of Thucydides' history, a passage he said that had often been referred to by China's President, Xi Jinping. He said regional peace and prosperity were intrinsically linked and dependent on co-operation between the US and China. At times during the speech Mr Turnbull closely echoed positions held by Barack Obama. As the President has, he urged observers not to exaggerate the power of the Islamic State, which he said was marked by "crazed delusions", but said the destruction of the self-styled caliphate was crucial to counter the terrorists group's "narrative of inevitable victory." Voicing a view also held by the White House he said boots on the ground were necessary to destroy IS, but they needed to be the "right boots on the right ground".

"The recent retaking of Ramadi is a good example," he said. "Led by the Iraqis themselves, assisted by the coalition's respective air and special forces, it was not just a blow to ISIL, but an example of the right combination. "An enduring victory must be won and owned by the people of Iraq and Syria." He said unless Sunni populations in Iraq and Syria could be reconciled in an inclusive order a stable peace could not be achieved. "The enmities are so deep, the wrongs so shocking, that every option should be on the table - from an institutionalised power-sharing to some form of partition," said the Prime Minister.

"This is a time for creative pragmatism and a recognition that difficult compromises will be required, particularly to avoid the sectarian aspect of this struggle spreading more widely across the region." With what appeared to be an eye turned to China Mr Turnbull said that online freedom was vital for democracy, human dignity and economic progress. "Australia, the US and others must work together internationally to promote norms of behaviour that are consistent with a free, open and secure internet," he said. "They include that states should not knowingly conduct or support cyber-enabled intellectual property theft for commercial advantage." Earlier in the day Mr Turnbull received a 19-gun salute and honor guard as he laid a wreath at the Tomb of the Unknown Soldier at Arlington National Cemetery before meeting Defence chiefs at the Pentagon.

The US Ambassador to Australia, John Berry, who attended the meetings, said there was no recrimination from the US due to Australia's recent decision not to increase its troop levels in the fight against the Islamic State. He said the first words out of the mouths of both the chairman of the Joint Chiefs, Joseph Dunford, and the Defence Secretary, Ashton Carter, upon greeting Mr Turnbull, were "thank you." He said America's call for increased support had been to all 60 members of the coalition fighting IS, not at Australia in particular, and that the US recognised that Australia had already made the second largest commitment to the effort after the US. During a question and answer session Mr Turnbull was asked how he was viewing the colourful presidential primary campaign. His voice being lost amid laughter Mr Turnbull responded that Australia would work well with whomever Americans "in their wisdom" elected. With AAP