Trump said he had a "productive discussion" with Turnbull on a wide range of issues in New York after he returned to the city for the first time since taking office.
He said they discussed the future of the two countries from the perspective of national security and trade to immigration and enhanced economic cooperation.
"We affirmed the tremendous friendship between the US and Australia," Trump said, adding that the reports that they had a rough telephone call on January 28 was exaggerated.
Trump's showering of praise came in stark contrast to what was reportedly a verbal spat between the two leaders over accepting refugees. Trump claimed the acrimonious call with Turnbull early in his White House tenure had been "fake news".
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Turnbull was among the first foreign leaders with whom Trump spoke with after taking office on January 20. Trump was reportedly irritated because he was expected to honour a deal made by his predecessor Barack Obama to accept more than 1,200 refugees.
Last month, Vice President Mike Pence visited Australia on a fence-mending visit. Although he too made it clear that Trump was not happy with the refugee deal, the US nonetheless would honour it.
At the patch-up meeting, Trump delivered a charm offensive through his speech at an event to honour the 75th anniversary of Australian and US victory in the Battle of the Coral Sea.
Trump said for nearly a century Americans and Australians have "fought together, bled together."
"Our two nations were born as the rebellious children of the same parent. Americans have had no better friends than the Australians, I mean that,"he said.
Trump thanked Australia, saying the US was "profoundly grateful" for its role to limit the conflicts in Syria, Iraq and Afghanistan.
Turnbull underscored the closeness of the two countries. "We are always more assured of winning when we are fighting together," he said.
On the refugee deal, he said, "We can put the refugee deal behind you and move on."