Mark McGowan has urged West Australians to distance themselves from "extremist" anti-vaxxers after two young men allegedly threatened to behead the premier and his family.
Police allege the men, aged 18 and 20, phoned Mr McGowan late on Saturday and left a number of threatening messages.
They have been charged with acts creating false apprehension as to the existence of threats or danger.
Both men have been bailed, subject to strict protective conditions, and are scheduled to face Armadale Magistrates Court next month.
The premier, his ministers and their staff have faced violent threats over the introduction of wide-reaching COVID-19 vaccination mandates.
"This is disturbing conduct. It's extremist conduct," Mr McGowan told reporters on Tuesday.
"I just urge them to stop it. It's not going to change our approach. We're going to continue to work to get West Australians vaccinated, we're going to continue with the rules we've put in place because that's what is needed.
"All this stuff is concerning, you can't say it's not. It's the sort of stuff that Islamic fundamentalists do in Syria - it's not the Australian way.
"I just urge everyone please, don't join with these anti-vaxxer extremist elements. Just get vaccinated."
Mr McGowan has indefinitely closed his electorate office in Rockingham, south of Perth, amid security concerns.
His personal phone number leaked in recent weeks and is believed to have been shared in anti-vaxxer group chats.
The premier said he would consider temporarily moving his family out of their Rockingham home, which has also been targeted by protesters.
"In terms of my own family, obviously it's not pleasant, it's not very nice and I'd just urge the people doing it to stop," he said.
Opposition Leader Mia Davies labelled the threats abhorrent and unacceptable.
The introduction of vaccine mandates by WA and other states has been vocally opposed by some federal politicians.
Five government senators crossed the floor of the upper house on Monday to support a One Nation bill to end the mandates. The bill was defeated in the Senate.
Prime Minister Scott Morrison has condemned violent protests but been accused of stoking tensions after last week saying it was time for "Australians to take their lives back".
WA Police Minister Paul Papalia said some of the public commentary around mandates was encouraging people to act in a "crazy, un-Australian fashion".
"It is reasonable to be concerned about the safety of the premier but also other public figures in this environment, when people who should know better are encouraging and giving comfort to this sort of behaviour," he said.
"It is wrong to suggest that governments are somehow doing anything else other than acting in the public interest by requiring people to get vaccinated.
"Getting vaccinated is what will protect the community from this threat of a pandemic ... that is the only reason governments are doing these things."
Police on Sunday were forced to hold back a crowd of anti-vaxxers who swarmed the premier's car as he attempted to leave a town hall event in the southwest WA town of Bunbury.
Several other cases remain before the courts, including that of a man charged over online threats to kill Mr McGowan and other political leaders.
The premier has insisted he won't be deterred from getting as many people vaccinated as possible.
"There's been death threats, there's been threats to rape my staff, there's been people threatening to bomb my office," he said last week.
"Someone turned up with an armoured car with a machine gun on the top. This is unbelievable conduct."
Australian Associated Press
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