Australia is considering moving its embassy in Israel from Tel Aviv to Jerusalem, Prime Minister Scott Morrison has announced, following the lead of US President Donald Trump.

Mr 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," Mr Morrison said.

He described proposals to recognise Jerusalem and move Australia's embassy as "sensible" and "persuasive" and would be considered by the government.

Israeli Prime Minister Benjamin Netanyahu issued a statement saying he had discussed the possible embassy move with Mr Morrison.

"He informed me that he is considering officially recognising Jerusalem as the capital of Israel & moving the Australian embassy to Jerusalem. I'm very thankful to him for this," Mr Netanyahu tweeted.

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 Mr Morrison's Liberal party, a former ambassador to Israel, is trailing in opinion polls.

A loss in the election would wipe out Mr 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.

Mr Morrison came to power in August after a revolt by hardline conservatives in the Liberal party ousted his more moderate predecessor, Malcolm Turnbull.

Mr Turnbull's government had explicitly distanced itself from the decision by Mr Trump to move the US embassy from Tel Aviv to Jerusalem as "unhelpful" to the peace process.

Mr Morrison rejected suggestions that his decision to consider following Mr Trump's lead was a result of US pressure or related to the by-election.

"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."

Mr 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.