Turnbull, who has clashed with Trump in the past, said their meetings Friday will set the stage for the "next 100 years of mateship", helping each country generate jobs and insure global security.
Turnbull says the meetings were a great opportunity to deepen Australia's engagement with its most strategic and economic partner.
"A lot of good things will come out of this", the president said.
The warmth was reciprocated by Mr Trump who declared: "The United States and Australia are now honouring 100 years of mateship, a term that you use very beautifully, Mr Prime Minister".
Prime Minister Malcolm Turnbull said he did not want to lecture America about gun control, after he was pressed on the politically fraught subject during a press conference with US President Donald Trump.
"But there is a possibility we would go in if there is a much better deal".
The two leaders haven't always seen eye-to-eye over the first 13 months of Trump's presidency.
Turnbull has called Joyce's affair a "shocking error of judgment". Putin was a pleasant call.
Mr Turnbull trod carefully, making it clear he was satisfied with Australia's gun laws, but declining to advise Mr Trump to follow a similar path.
At a comedic press dinner previous year, Turnbull mocked Trump's obsession with "winning" online polls.
The two men are also divided on trade.
Turnbull is trying to lure Trump back into the TPP.
The leaders spoke in the Oval Office during a portion of the meeting that was open to US and Australian journalists.
Turnbull's visit to the White House followed tense interactions between the two leaders previous year, when they clashed over a refugee swap deal.
As he sat with Mr Turnbull in the Oval Office, Mr Trump said: "The relationship we have with Australia is a terrific relationship and probably stronger now than ever before".
"We're working on a trade deal, we are working on military and protection", Mr Trump said.
Mr Turnbull said it was the 100th anniversary of the World War I battle for Hamel in France where Australian and U.S. forces first fought together.
"We have been fighting side by side in freedom's cause ever since".