The Washington Post said Trump abruptly cut short the fiery conversation after criticising the agreement to re-settle people kept in Pacific camps, sparking a war of words with Australian Prime Minister Malcolm Turnbull today after the report surfaced.
Australia is considered a close US ally -- one of the so-called "Five Eyes" with which the US routinely shares sensitive intelligence -- and the call might have been expected to be smooth sailing.
Of his four conversations with world leaders that day "This was the worst call by far," it cited him as telling Turnbull, shortly before he terminated the telephone meeting.
Australian government sources told the Australian Broadcasting Corporation the report was "substantially accurate".
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Turnbull said he was disappointed details of the "very frank and forthright" exchange had been leaked.
"As far as the call is concerned I'm very disappointed that there has been a leak of purported details of the call in Washington," he told Sydney radio station 2GB.
"But I want to make one observation about it -- the report that the president hung up is not correct. The call ended courteously."
The Post's account is markedly different from the official read-out of the call provided by both governments.
Turnbull said Monday that Trump had agreed to honor the deal struck with then president Barack Obama to resettle an unspecified number of the 1,600 people Australia holds in offshore processing centers in Nauru and Papua New Guinea.
There were fears the new US president would rescind it after he signed an executive order last week to suspend the arrival of refugees to the US for a least 120 days, and bar entry for three months to people from seven Muslim-majority countries.