US President Donald Trump threatened a "very rough day" for North Korea as his administration announced harsh new sanctions against the rogue state.

The Trump administration is hitting more than 50 vessels, shipping companies and trade businesses with sanctions in the latest bid to turn up the pressure on North Korea over its nuclear program, according to a senior administration official.

Speaking alongside Prime Minister Malcolm Turnbull today, Mr Trump spoke about the danger of the North Korean regime's program.

He threatened dire consequences if the country did not come to heel.

"Phase two may be a very rough day," Mr Trump said.

"May be very, very unfortunate for the world."

The subject was one of a number under discussion when the two leaders met in the US.

Mr Trump praised the US relationship with Australia, saying the two nations were honouring "100 years of mateship".

He used Australia's immigration policies as a spur to the other levels of US government, which has proven intransigent in passing Mr Trump's full immigration measures.

"Merit-based immigration. Are my friends from Congress listening to that?" he said.

However, Mr Trump remained negative on the Trans-Pacific Partnership Agreement, saying it was a "very bad deal" for the US.

He and Mr Turnbull also agreed that a Port Arthur-style gun buyback program would not work in the US as it had in Australia following the 1996 massacre.