They also include banning textile imports.
Meanwhile, Russia and China have staged naval exercises ahead of a UN General Assembly meeting where North Korea's nuclear ambition is likely to dominate proceedings.
Nikki Haley, the USA ambassador to the UN, said on Sunday the UN Security Council has run out of options on containing North Korea's nuclear programme - and the U.S. may now turn to the Pentagon.
Pyongyang says it will not give up on its nuclear deterrence unless Washington ends its hostile policy toward the country and dissolves the US-led United Nations command in South Korea.
At the same time, Haley said the U.S.is "a country of laws".
Ms Bishop declined to comment on reports the Central Intelligence Agency asked Australia to set up a diplomatic presence in North Korea.
The two leaders "committed to maximising pressure on North Korea through vigorous enforcement of United Nations Security Council resolutions", a statement said.
Trump called it "an outrage" that some nations continue to trade with North Korea.
North Korea has launched a trio of missiles in recent weeks and tested a bomb that was its most powerful to date.
On Sunday, US Air Force flew B-1 bombers and F-35 stealth fighter jets over the Korean Peninsula with allied fighter jets from South Korea and Japan.
Now, I said yesterday I am perfectly happy kicking this over to General Mattis, because he has plenty of military options.
The global community is scrambling to contain an increasingly belligerent Pyongyang, which has conducted its sixth and largest nuclear test and fired long-range missiles over Japan that it says could reach the USA mainland.
"Definitely, there is no military solution there, no doubt that if any military operation is carried out, unfortunately, North Korea's authorities will fulfill those possibilities that they have", Kosachev stressed.