The failed test was North Korea's ninth missile launch since Trump took office in January.
South Korea's defence ministry said it suspected Saturday's missile test had failed after a brief flight, while the USA military's Pacific Command confirmed the rocket did not leave North Korean territory.
Mr Turnbull will meet Mr Trump for the first time Thursday in NY.
Meanwhile, on Friday, Tillerson warned of "catastrophic consequences" if the U.N. Security Council did not act, saying it was "likely only a matter of time before North Korea develops the capability to strike the USA mainland".
Tensions have rapidly escalated in highly volatile region since President Donald Trump declared he would be prepared to act "unilaterally" against Pyongyang in early April.
President Trump didn't answer reporters' questions about the launch when he returned to the White House from Atlanta, but later admonished Pyongyang via Twitter.
"The key to solving the nuclear issue on the peninsula does not lie in the hands of the Chinese side", Wang said.
The United States and South Korea say THAAD is crucial to counter North Korea's weapons advances. "And I will tell you a man that I have gotten to like and respect, the president of China, President Xi, I believe has been putting pressure on them also, but so far, perhaps nothing's happened, perhaps it has".
The arrival of both vessels in the region was described as a show of force in advance of a long-anticipated sixth nuclear test from the North Korean government.
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South Korea's Joint Chiefs of Staff said in a statement that the missile flew for several minutes and reached a maximum height of 71 kilometres (44 miles) before it apparently failed.
The American Pacific Command confirmed the missile did not leave North Korean territory and was not seen as a threat to the United States.
A United States official said the ballistic missile, thought to be a mid-range KN-17, was sacked from a location in the South Pyeongan province in the early hours of Saturday morning local time. The North fired the same type of missile April 16, just a day after a massive military parade where it showed off its expanding missile arsenal, but USA officials called that launch a failure.
Inter-continental ballistic rockets will fly into the United States "if the U.S. shows any slight sign of provocation", the newspaper said.
U.S. Secretary of State Rex Tillerson says China has asked North Korea to conduct no further nuclear tests.
South Korean officials also said the test likely was a failure.
"Something that's ready to go could be taken from the larger package and expedited".
"If he does a nuclear test, I will not be happy", said Trump.
Kim Jong-un attempted to launch what is believed to be a mid-range ballistic missile from a site north of his capital in Pyongyang on Friday.