Australian Foreign Minister Julie Bishop called the message "unprecedented," noting that North Korea usually chooses different means to communicate.
Her office confirmed to CNN that the letter published by The Sydney Morning Herald
The document, dated September 28, appears to have been distributed about a week after Trump's address
to the United Nations General Assembly, when he said "the United States has great strength and patience, but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea."
In the letter, North Korea condemned that statement as tantamount to a declaration of war, something North Korean officials said
shortly after the speech. The United States denied that Trump had declared war on North Korea, which is also known as the Democratic People's Republic of Korea.
The letter said: "If Trump thinks that he would bring the DPRK, a nuclear power, to its knees through nuclear war threat, it will be a big miscalculation and an expression of ignorance."
Australian Prime Minister Malcolm Turnbull called the letter "basically a rant about how bad Donald Trump is" during an interview with 3AW Mornings with Neil Mitchell.
"It's North Korea that is threatening to fire nuclear missiles at Japan and South Korea and the United States. It's North Korea that is threatening the stability of the world," Turnbull said.
Bishop posted a copy of a cover letter on her verified Facebook page.
Both Bishop and Turnbull said Friday they believe the letter shows that North Korea is getting desperate as the US and its allies ramp up sanctions on the rogue regime.
"I see it as evidence that the collective strategy of imposing maximum diplomatic and economic pressure through sanctions on North Korea is working," Bishop said.
Recent UN sanctions have targeted everything from seafood exports, foreign labor and joint ventures with North Korea.
In the United States, the Trump administration has made it clear that it plans to go after North Korea's money abroad as part of its pressure campaign, in the hopes the regime will consider putting its nuclear weapons and missiles on the negotiating table.
Regardless of whether the strategy succeeds, analysts are split about whether choking off North Korea's revenue will push leader Kim Jong Un to give up his arsenal or double down on perfecting it. North Korea believes nuclear weapons are the ultimate deterrent against any potential US-led attempts at invasion or regime change.
As it inches closer to arming a long-range missile with a nuclear-tipped warhead, North Korea has warned US allies that their support for Washington could prove costly.
North Korea has continually assailed Australia as a "vassal country" of the United States in recent releases from North Korean state media.
Earlier this month, a spokesman for the North Korean Foreign Ministry told the country's state-run Korean Central News Agency
(KCNA) that Australia's support for the United States in opposing North Korea was a "suicidal act."
"Australia will be unable to avoid a disaster if it keeps toeing the US line of military, economic and diplomatic pressure upon the DPRK despite its repeated warnings," the Foreign Ministry spokesman was quoted as saying.
"It should be prudent in speech and conduct with its own principle, instead of blindly following the US' policy of aggression, and realize that working to develop friendly relations with other countries is the best way to its security."
Those threats have not stopped Turnbull and Bishop from voicing their support for Trump's pressure strategy on North Korea.