"He informed me that he is considering officially recognizing Jerusalem as the capital of Israel & moving the Australian embassy to Jerusalem". Israel closed its embassy in Asuncion in response.
But Morrison denied the United States influenced his announcement.
The Palestinians, with broad worldwide backing, want East Jerusalem as the capital of a future state that they hope to establish in the occupied West Bank and the Gaza Strip.
The status of Jerusalem is perhaps the thorniest issue in the Israeli-Palestinian conflict.
Like Trump, Morrison and Payne vaguely said they might recognize "Jerusalem", without adding geographical or political adjectives. He reiterated support for a two-state solution.
The two-state solution envisages an independent Palestine alongside Israel. Currently, only the United States and Guatemala have their diplomatic headquarters there.
At the same time, it must be noted that the new Australian government is not about to recognize Palestinian statehood. Peace talks between the parties broke down in 2014.
As Scott Morrison stood accused of ditching 70 years of Australian foreign policy and reports emerged that Indonesia may suspend a planned bilateral trade deal, the prime minister told parliament no firm decision had been taken.More news: Khashoggi killed in interrogation 'gone wrong'
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"You can achieve both" the two-state solution and Jerusalem being Israel's capital, he claimed. "Can we transfer our representative office in Ramallah, which is not yet an embassy, to East Jerusalem?"
"No decision has been made in regarding the recognition of a capital or the movement of an embassy. but at the same time, what we are simply doing is being open to that suggestion".
Whether Australia will end up recognizing Jerusalem - or West Jerusalem - is still open.
The surprise announcement came just days before a crucial parliamentary by-election in a Sydney district that has a significant Jewish electorate and where the candidate for Morrison's Liberal party, a former ambassador to Israel, is trailing in opinion polls.
He described proposals to recognise Jerusalem and move Australia's embassy as "sensible" and "persuasive" and would be considered by the government.
This pressure, too, might put the kibosh on Morrison's plan.
Asked about the government's review of the agreement, which the Israeli government has vehemently opposed, Mr Sofer said Australia is a major player on the worldwide arena.
"The review will reassess whether the Plan remains the best vehicle to address the worldwide community's concerns about Iran's nuclear ambitions", the joint statement said.
Mr Morrison has also announced the government would review Australia's support for the Iran nuclear deal to see whether it was still "fit for purpose" in preventing the country from acquiring nuclear weapons after Mr Trump withdrew the U.S. from the Obama-era deal.