Morrison called a press conference to say he was "open-minded" to proposals to formally recognise Jerusalem as the capital of Israel and move his nation's embassy to the holy city, a sharp break with the policy of successive Australian governments for decades.
"We're committed to a two-state solution, but frankly it hasn't been going that well, not a lot of progress has been made, and you don't keep doing the same thing and expect different results," Morrison said.
He described proposals to recognise Jerusalem and move Australia's embassy as "sensible" and "persuasive" and would be considered by government.
The surprise announcement came just days before a crucial parliamentary by-election in a heavily Jewish Sydney constituency where the candidate for Morrison's Liberal party, a former ambassador to Israel, is trailing in opinion polls.
A loss in the election would wipe out Morrison's one-seat majority in parliament.
"Scott Morrison is now so desperate to hang on to his job, he is prepared to say anything if he thinks it will win him a few more votes -- even at the cost of Australia's national interest," said the opposition Labour party foreign policy spokeswoman Penny Wong.
Morrison came to power last month after a revolt by hardline conservatives in the Liberal party ousted his more moderate predecessor, Malcolm Turnbull.
Morrison rejected suggestions that his decision to consider following Trump's lead was a result of US pressure or related to the by-election in Sydney's Wentworth district on Saturday.
"I have made this decision without any reference to the United States," he said. "It has not come up in any discussion that I have had with the president or officials."
Trump's move ruptured decades of international consensus that Jerusalem's status should be settled as part of a two-state peace deal between Israel and the Palestinians.