The Korean Central News Agency (KCNA) added that Trump expressed his intention to suspend all joint military drills between South Korea and the US while talks are under way between Pyongyang and Washington.
"I don't believe that suspension for suspension has actually been agreed", Ms Bishop said on Wednesday.
The emerging detente between U.S. and North Korea represents a step forward in world peace.
Before the unexpected thaw between Pyongyang and the US, North Korea had repeatedly threatened to target US troops in the region.
"The war games are very expensive", Trump said.
Speaking briefly, hours after the historic talks in Singapore, Abe also said he was pleased that the USA leader had raised the emotive issue of Japanese abducted by Pyongyang.
She also defended "the right of our allies to carry out military exercises" and pointed to Australian involvement in other multilateral drills.
If anything, shipping saw some small benefit from the moves to isolate North Korea economically.
In his second and last telephone conversation with Mr Trump in just two days, Moon offered to discuss a joint excavation programme with North Korea to recover the remains of USA soldiers killed or captured in the Korean War, Cheong Wa Dae said earlier. "I thought they were very provocative".
Japan would continue joint military exercises with the USA and would stick to plans to bolster its defences against a possible ballistic missile strike from North Korea.
He praised Mr Trump and Mr Kim for their "courage and determination" not to settle for "that outdated and familiar reality but to take a daring step towards change".
The summit's joint declaration said that Pompeo and North Korean officials would hold further talks "at the earliest possible date".
North Korean leader, Kim Jong-un, visits the Marina Bay Sands hotel in Singapore on Monday.
President Moon Jae-in is expected to be briefed personally by the U.S. secretary of state, who landed at Osan Air Base.
If China decides to follow Trump's lead and dial back sanctions, then Tooth says North Korea's coal exports could ramp right back up.
As for whether clients are approaching him on doing deals in North Korea, "the answer is no", Paulsen said.
But Mr Trump's announcement of an end to joint war games caught South Korea by surprise.
Highlighting the central role for China, which is a close ally of North Korea, the Chinese foreign minister said, "I don't think anyone would doubt the unique and important role China has played in this process, and it will continue to play".