During a joint news conference with Turnbull, Trump said he and his Australian partner are celebrating "100 years of mateship", a century-long relationship that now includes cooperation on counter-terrorism, trade, immigration and efforts to pressure North Korea to give up nuclear weapons.
Mr Trump said he hopes to follow Australia with its tough "merit-based" immigration policies and announced the U.S. would name a new combat ship the USS Canberra.
President Donald Trump continued his calls to arm more teachers with guns to protect schools in a joint news conference with Australian Prime Minister Malcolm Turnbull on Friday.
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".
It was not always so.
Diplomats - and even a mutual friend, golfer Greg Norman, who was at the White House on Friday - rushed to fix the damage.
Washington will honour the deal to take up to 1,250 asylum-seekers held in Australian detention centres on remote Pacific islands, so Trump and Turnbull will now seek to find common ground on China and the Trans-Pacific trade pact, which aims to cut barriers in some of the region's fastest-growing economies.
Turnbull, a former Goldman Sachs banker, thanked Trump and Melania for their "hospitality and friendship".
The visit is founded on the idea of "mateship", stemming back 100 years to when Australian and American troops fought together for the first time. The prime minister predicted 100 more years of friendship to come.
"We have been fighting side by side in freedom's cause ever since".
The pair have met since the infamous call, most notably in May aboard the Intrepid, moored in NY.
"We're working on trade deals, we're working on military and protection and all of the things that you would think we would be discussing today".
Australia's embattled deputy prime minister, under pressure over an extramarital affair, faced a call to step down as leader of his party on Thursday, the first such call from a member of the party, which is part of the ruling coalition.