Foreign Minister Penny Wong told ABC's Insiders program on Sunday everyone wanted to "take the next steps towards a ceasefire" but warned such action could not be "one-sided".
Senator Wong said Israel should observe international law, citing Australia's concerns with the deaths of civilians in struggling and under-threat Gazan hospitals.
However, Senate Nationals Leader Bridget McKenzie claimed Senator Wong's comments were an "equivocation".
"Calling for a ceasefire as if there was some equivalence between the actions of Hamas and the actual reality of war is absolutely appalling and it needs to be highly condemned," she told Seven's Sunrise program on Monday.
But Environment Minister Tanya Plibersek clarified that Senator Wong said "we should be working towards the ceasefire" rather than outright pushing for an end to violence, and reiterated Israel's "right to defend itself".
"We should be seeking to minimise civilian casualties, particularly in hospitals and those vulnerable facilities even Gaza," she told Sunrise on Monday.
"Working towards a ceasefire, calling for humanitarian force - that is a recognition that the civilian casualties in Gaza at the moment are very high, unacceptably high."
Palestinian officials said two babies were killed following Israeli strikes at the Al-Shifa hospital complex as the number of Gazans killed by the Israeli bombing and blockade campaigns climbed to more than 11,000.
Israel has said Hamas, which has been labelled a terrorist organisation by the federal government, has command centres under and around the hospital.
Members of the Jewish community held a vigil in Sydney for people taken hostage in the war.
Large demonstrations took place again across Australia at the weekend, with Victoria police saying 45,000 people attended a pro-Palestinian rally outside the state library in Melbourne.
The rally on Sunday followed violent clashes on Friday night after a Palestinian business in Caulfield in the city's southeast was firebombed.
Owner Hash Tayeh addressed the crowd on Sunday, saying the "cruel" act of arson reduced his store to ashes.
"To those who sought to silence us with hate and violence, I say you will not succeed," he said, while draped in a Palestinian flag.
"Love and unity will always prevail."
A survey published last week by pollster YouGov found 53 per cent of Australians supported an immediate ceasefire between Israel and Hamas, compared to 26 per cent who did not.
Roads were closed in Sydney's CBD for the fifth weekend in a row as a pro-Palestinian demonstration took place in Hyde Park, while members of the Jewish community gathered in Moore Park to hold a vigil for people taken hostage in the war.
Liberal MP Julian Leeser plans to wear a kippah head covering when parliament sits this week.
Executive Council of Australian Jewry co-chief Alex Ryvchin called for the destruction of Hamas, the safe rescue of every hostage and peace "for the land of Israel".
Liberal Party MP Julian Leeser said he would wear a Jewish kippah head covering this sitting week, saying he hoped it would "remind the parliament that our country is made up of people of many faiths as well as those with none at all".
Rallies were also held in other cities and towns, including at Brisbane's King George Square and outside Parliament House in Perth and Russell Square in Adelaide on Sunday.
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