US PRESIDENT Donald Trump may soon visit Down Under, praising the “terrific” relationship between America and Australia during a White House meeting with Prime Minister Malcolm Turnbull.

The pair met at the Oval Office early yesterday morning, with Mr Trump and Mr Turnbull discussing key issues of economic and regional security, including tax reform, the Trans Pacific Partnership and how the alliance was managing tensions with China and North Korea.

The meeting came as the US announced strict new sanctions on the North Korean regime aimed at cutting off smuggling routes that defy current UN sanctions.

Praising Australia as a key ally in a campaign of “maximum pressure” on Pyongyang, Mr Trump warned that if sanctions failed, there would be a “phase two” inflicted on the rogue nation.

“If the sanctions don’t work, we’ll have to go to phase two. Phase two may be a very rough thing. It may be a very unfortunate thing for the world,” Mr Trump said at a joint media conference with Mr Turnbull at the White House.

On China, Mr Trump said he would like to see Australia assist with freedom of navigation exercises in the South China Sea, a manoeuvre so far resisted by Australia given it would spark tensions between Canberra and Beijing.

“We would love to have Australia involved and I think Australia wants us to stay involved,” Mr Trump said.

Mr Trump said the US and China had a very strong relationship, but warned lopsided trade between the two countries was a risk.

“China is tough, they’re getting stronger to a large extent from a lot of the money they’ve made from having poor leadership in the US because the US leadership has allowed them to get away with murder,” he said. “I have to say we have developed a great relationship with China, other than the fact they had been killing us on trade for a long period of time.”

Despite Australia hoping to win over the US on the Trans Pacific Partnership, which is being pursued by the 11 other Pacific rim countries despite America’s withdrawal, Mr Trump said it was not a good deal.

“TPP was a very bad deal for the United States — it would have cost us a tremendous amount of jobs, but there is a possibility I would go in but they will be offering us a much better deal,” he said.

“I like bilateral deals much more than multilateral — you negotiate with one country and if it doesn’t work out, you terminate.”

While the two leaders saw eye to eye on most foreign policy issues, Mr Turnbull was reluctant to engage in the domestic debate raging in America over gun law reform in the wake of the Florida school shooting that left 17 dead.

When asked by the American media about Australia’s gun crackdown after the Port Arthur massacre in 1996, Mr Turnbull said semi-automatic and automatic weapons were “essentially not available” in Australia following the reforms. But he also said that Australia’s history with gun control was “very different” to America’s.

With the visit conducted under the banner of “100 years of mateship” between Australia and the US, Mr Trump announced one of the new Littoral Combat navy ships being built for the US Navy by WA shipbuilder Austal would be named the USS Canberra.

When asked if he would soon like to visit Australia, Mr Trump said, “I would, absolutely”.

“Love it. We will be there, (it is a) great place”.