However, given that one of Indonesia's foremost foreign policy positions is support for a Palestinian state, Mr Morrison's declaration in support of Jerusalem as Israel's capital has not gone down well in Jakarta. Israel closed its embassy in Asuncion in response.
The two leaders also discussed strengthening bilateral relations, deepening defense ties and a prospective agreement to appoint military attaches to both embassies.
Despite the controversial move, Morrison appeared to voice his commitment to a two-state solution to the Israeli-Palestinian conflict.
Mr Howard also said he "remains a strong critic" of the Iran nuclear deal, which Mr Morrison has also vowed to review.
Former Prime Minister Malcolm Turnbull and Foreign Minister Julie Bishop had rejected the proposal when it was urged on them by the Government's conservative wing earlier this year, in the wake of US President Donald Trump's decision to make the same move.
Former senior diplomat John McCarthy, who has served as Australia's ambassador in Jakarta, said any decision to move the embassy from Tel Aviv to West Jerusalem would be "very poorly regarded internationally". According to Egypt's envoy Mohamed Khairat, recognition of Jerusalem as the Israeli capital could damage the peace process in the Middle East.
In a statement, Palestine's embassy in Australia called Morrison's announcement "deeply disturbing". It's a bit cute to say its consistent with a two-state solution. "It might increase the chances of the government winning Wentworth in Australia", he said.
Prime Minister Scott Morrison, left, speaks to the media alongside Minister for Foreign Affairs Marise Payne during a press conference at the Parliament House in Canberra, Tuesday, October 16, 2018. "We support a two-state solution and our view has been that any shift in representation, in the way we saw with the United States, does not move us closer to that peaceful resolution", she said. They suspected that the politician was trying to make some political gains, which "would surely be outweighed by the detriment both to Australia's worldwide standing and in its relations with Arab and Muslim-majority countries".
"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.
Worldwide consensus has been that Jerusalem's status should be settled in a peace deal and recognising it as a capital for either side would prejudice one party over the other.
Sharma, who was ambassador to Israel between 2013 and 2017, is on Saturday standing as a candidate for Morrison's ruling Liberal Party in a crucial by-election in Sydney.
While not a signatory to the 2015 landmark nuclear pact with Iran, Australia reversing its current support of the deal, and possibly supporting the United States sanctions on Tehran, would greatly please Israel - probably even more than a recognition of West Jerusalem as its capital.