Israeli Prime Minister Benjamin Netanyahu tweeted his approval on Monday.
Turnbull's government had explicitly distanced itself from the decision by Trump to move the USA embassy from Tel Aviv to Jerusalem as "unhelpful" to the peace process.
"We're committed to a two-state solution", Mr Morrison told a media conference in Canberra.
"The short-term political gain that could be secured by moving the Australian embassy from Tel Aviv to Jerusalem would surely be outweighed by the detriment both to Australia's global standing and in its relations with Arab and Muslim-majority countries and the worldwide community more broadly", the delegation said.
"Foreign policy, and Australia's national interest are far too important to be played with in this fashion", she said.
Morrison rejected suggestions that his decision to consider following Trump's lead was a result of United States pressure or related to the by-election in Sydney's Wentworth district on Saturday.
Australia would be the second major country, after the United States, to make such a move.
"The whole point of a two-state solution is two nations recognised living side by side", he added, saying he was open to the suggestion from Dave Sharma, Australia's former ambassador to Israel, that Australia support West Jerusalem as Israel's capital and East Jerusalem as Palestine's. Sharma is the Liberal candidate in Wentworth, a district where voters - 13 percent of whom are Jewish - may end up determinig whether the Liberals maintain the seat.
The status of Jerusalem is one of the thorniest obstacles to a peace deal between Israel and the Palestinians.
"What I am doing today is recognising what is a real concern in the Jewish community in Australia - whether it is about the Iran nuclear deal, which is an item of great concern to that community, or it is on this broader question of the two state solution and how with go about achieving it".
Australia and Israel will appoint defence attaches in respective embassies.