Scott Morrison has raised concerns about escalating violence between Israel and Palestine, which the United Nations fears could explode into full-scale war.
The Prime Minister has also expressed disappointment after a woman was charged in western Sydney for burning an Israeli flag.
Dozens of people have been killed in the worst violence between Israelis and Palestinians in several years and which shows no sign of letting up.
The conflict flared up after Israeli forces tried to forcibly evict Palestinians from their homes in the neighbourhood of Sheikh Jarrah and stormed the al-Aqsa mosque in Jerusalem.
Mr Morrison said it was important the conflict in the Middle East did not spill onto the streets in Australia.
“Of course we are all very concerned about what is happening there,” he told 2GB radio on Thursday.
“We have been urging restraint from all parties involved there to not take any unilateral action on those very stressful and tense situations we are finding there.
“But those things should not be played out here in Australia.”
Mr Morrison restated the government’s policy of a two-state solution between Israel and Palestine, describing Australia as an agent for peace.
He urged Australians with ties to the conflict to act with tolerance and respect.
“By all means, people can have concerns and views, and there is a tolerance for that, but at the same time we do not want to import the troubles of other parts of the world into this country.”
Meanwhile, Israel’s president warned of a civil war between the country’s Arabs and Jews as fury and fear over shelling exchanges with Palestinian militants in Gaza ignited violence in Israel’s streets.
Appeals by religious and political leaders for calm, and police reinforcements and mass-arrests, appeared to do little to stem riots in several ethnically mixed towns.
Israeli TV showed what it described as “near-lynchings” of Jewish and Arab motorists.
The strife was touched off by sometimes violent pro-Palestinian protests by members of the Arab minority incensed at an Israeli air barrage launched on Gaza on Monday after Islamist Hamas-led militants fired salvoes of rockets across the border.
At least 65 Palestinians and six people in Israel have since died in the heaviest exchange of air strikes and rocket fire since the two sides fought a war in 2014.
UN diplomat Tor Wennesland urged restraint from both sides.
“Stop the fire immediately. We’re escalating towards a full-scale war,” he tweeted.
“The cost of war in Gaza is devastating and is being paid by ordinary people. UN is working with all sides to restore calm. Stop the violence now.”
Various countries including the United States have also called for calm.
A synagogue and cars were torched in the Tel Aviv suburb of Lod, motorists were stoned on some roads, and Palestinian flag-waving protesters scuffled with police in northern Haifa port.
By Wednesday, police said the assaults appeared to be more by Jews against Arabs, including one seen on live TV as he was dragged from his car and pummelled by a mob in coastal Bat Yam.
The broadcast on the top-rated Channel 12 cut to a phoned-in appeal by President Reuven Rivlin to “please stop this madness”.
“We are endangered by rockets that are being launched at our citizens and streets, and we are busying ourselves with a senseless civil war among ourselves,” said the president, whose role is largely ceremonial.