Pro-Palestinian encampments have been set up at several universities following protests in the US, calling for tertiary institutions to divest funds from Israel and for a ceasefire in Gaza.
Tensions have heightened following the arrival of Israeli supporters near the sites.
The prime minister is alarmed by divisions over the conflict in Australian society.
"Social cohesion is being frayed at the moment, I'm very concerned at what we've seen," he told reporters on Monday.
"There has been a rise in anti-Semitism, there has been a rise in Islamophobia.
"We need to make sure people in positions of authority use that authority to not promote division but to promote social cohesion.
"It's really important also that people don't seek to bring conflict, which is here in Australia."
The pro-Palestine encampment at the University of Sydney. (Dean Lewins/AAP PHOTOS)
University vice-chancellors have rejected calls for police to break up the protests.
Federal Education Minister Jason Clare has received reports of students afraid to attend campuses.
"If people feel afraid to go to university then that's intolerable. I want more people to go to university, not less," he said.
There would always be a place for protests in a democratic society, Mr Clare said.
"What there's no place for though is hate or violence or prejudice or discrimination, and certainly no place for anti‑Semitism or Islamophobia."
Mr Clare repeated calls to lower the temperature of debate about the conflict.
"What's happening on the other side of the world is trying to pull our country apart," he said.
"We've got to work together - whether it's politicians or religious leaders or community leaders, whether it's the media or student representatives - to work to keep our country together, not let it get pulled apart."
Members of the Jewish community gathered outside the University of Melbourne last week. (Joel Carrett/AAP PHOTOS)
Opposition spokeswoman Sarah Henderson called for hate speech to be banned on university campuses, saying the government was not doing enough to stamp it out.
"The level of hate speech, intimidation and harassment against Jewish students and staff and visitors on university campuses is absolutely appalling," she said.
"The encampments must go, the codes of conduct must be enforced.
"The prime minister must step in and force this helpless and hopeless education minister to ensure Jewish students are safe at universities."
The university protests centre on Israel's war on Gaza.
Hamas, considered a terrorist organisation by the federal government, attacked Israel on October 7, killing an estimated 1200 people and taking more than 250 hostages.
In response, the Israeli military has killed more than 34,000 Palestinians and injured at least 77,000 others, according to the local health ministry.
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