The two-state solution envisages an independent Palestine alongside Israel.
"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 told reporters after calling an unexpected press conference.
The BBC also cited the premier as saying that one future scenario could involve Australia recognizing a Palestinian capital in East Jerusalem al-Quds and an Israeli capital in West Jerusalem al-Quds.
Labor reminded the government that Frances Adamson, the head of Australia's foreign department, said in June that the US move had "not been helpful" for the Middle East peace process.
Australia has raised the prospect of following the United States by relocating its embassy in Israel from Tel Aviv to Jerusalem in a policy shift that critics described Tuesday as a desperate grab for domestic political gain to win a crucial byelection. US President Donald Trump's daughter, Ivanka Trump, attended the ceremony.
Like Mr Morrison, Indonesia's President Joko Widodo is facing an election next year.
"Indonesia conveys our strong concern on the announcement and question the merit of the announcement", Indonesian Foreign Minister Retno Marsudi said, referring to the potential embassy move.
Australia may be moving its embassy in Israel from Tel Aviv to Jerusalem to follow the Trump administration in recognizing the Holy City as the nation's capital.
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"They have a trade imbalance as capital flees Indonesia, and the President, I feel, has been very keen to demonstrate he has a good economic base where he wants to take the country", he said.
'Foreign policy, and Australia's national interest are far too important to be played with in this fashion, ' Senator Wong said.
Census figures show 12.5% of people in Wentworth are Jewish, a significantly larger proportion than the rest of the country.
The anticipated announcement comes as Australia's former envoy to Israel David Sharma, plans to run as a Liberal candidate for a key parliamentary seat in the Wentworth district of New South Wales; a heavily Jewish area that was left vacant after Prime Minister Malcolm Turnbull resigned last month.
"I have made this decision without any reference to the United States", he said.
Mr Trump's decision enraged Palestinians and upset the Arab world and Western allies like.
The Wentworth vote is scheduled for Saturday.
Palestinians, with broad worldwide backing, want East Jerusalem as the capital of a future state they hope to establish in the occupied West Bank and the Gaza Strip.
If the embassy move is realized, Australia would become the third country in the world to have its envoys based in the disputed city. Peace talks between the parties broke down in 2014.