Climate advocate Greta Thunberg was among a dozen activists on board the Freedom Flotilla Coalition's vessel Madleen when it was intercepted by Israeli forces in the Mediterranean Sea early on Monday.
They were prevented from entering the blockaded enclave.
Students for Palestine, one of the groups that called for a snap protest at the prime minister's electorate office in Sydney among others around the country, said Australia should expel the Israeli ambassador.
"The Madleen crew represent the hopes of all those who stand for humanity against the starvation and bombardment of Gazans, and they must be immediately released," the group's co-convenor Jasmine Duff said on Monday.
Carrying placards and umbrellas on a rainy Monday they vocalised their anger and demanded Australia diplomatically increase pressure on Israel.
"We call on Anthony Albanese and Penny Wong to immediately expel the Israeli ambassador, cut all military and economic ties with Israel, and pressure Israel to release the illegally kidnapped crew," Ms Duff added.
The Sicily-based coalition said the humanitarian boat was "unlawfully boarded, its unarmed civilian crew abducted, and its life-saving cargo - including baby formula, food and medical supplies - confiscated."
But the Israeli foreign ministry pointed the finger at Thunberg saying it was a "selfie yacht of celebrities" and those on board would be deported to their home countries.
The progressive Jewish Council of Australia also urged Australia to place sanctions on Israel.
"The world is watching," the council's executive officer Sarah Schwartz said.
"We don't have to be a 'major player' to show our commitment to the basic humanity of Palestinians and be part of the global movement to pressure Israel through sanctions to comply with international law,"
The lack of food reaching Gaza caused by Israeli aid obstruction is leaving hundreds of thousands of Palestinians "vulnerable to starvation", the United Nations warned earlier in June.
More than 54,000 Palestinians have been killed in Israel's ongoing military offensive, according to Gaza health officials.
The retaliatory campaign was in response to Hamas militants killing 1200 Israelis and capturing more than 250 hostages in October 2023.
Israel has imposed a naval blockade on the coastal enclave since Hamas took control of Gaza in 2007.
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