Malcolm Turnbull says new citizens also need to be "Australian patriots", as he seeks to underline his government's commitment to tackling terrorism.
The prime minister on Tuesday delivered a national security statement to parliament.
In his speech he updated the nation on the challenges facing Australia at home and overseas but reassured Australians the government was staying ahead of the evolving threat from Islamist extremists through a range of means.
Mr Turnbull told parliament Australia is not immune from the global impact of the conflicts in the Middle East and instability around the world.
"But we should also be reassured - our law-enforcement agencies, intelligence services and Australian Defence Force are among the best in the world," he said.
"We lead our Australian way of life on our terms. We will not buckle or be cowed by this scourge of Islamist terrorism."
This week the government will introduce to parliament laws to change visa and citizenship requirements.
Mr Turnbull urged Labor to pass the laws.
"There is no more important title in our democracy than 'Australian citizen," he said.
"And we should make no apology for asking those who seek to join our Australian family to join us as Australian patriots - committed to the values that define us, committed to the values that unite us."
Borrowing a line from John Howard, Mr Turnbull said: "Our success as a multicultural society is built on strong foundations which include the confidence of the Australian people that their government, and it alone, determines who comes to Australia."
PM announces new citizenship rules
Since August 2014 the government has invested $1.5 billion in law enforcement and security agencies to combat terrorism and passed eight tranches of legislation.
On the battlefield, Islamic State has lost 55 per cent of the territory it previously held in Iraq and Syria.
On the online front, Attorney-General George Brandis is set to work with overseas colleagues on ways to crack down on terrorists and organised criminals using what Mr Turnbull describes as "ungoverned digital spaces".
Opposition Leader Bill Shorten, in his reply, will call for Facebook and Twitter, as well as the developers of encrypted communications apps, to do more in the counter-terrorism space.
"Facebook has created new dedicated teams and employed thousands of people specifically to monitor its Facebook Live stream and remove offensive content.
"But we need more - and these companies have the resources and the capacity to do more.
"Terrorists don't self-police, so we cannot rely on a self-policing system."
He will also call for better co-operation between the federal and state governments to protect communities and detect and prevent terrorist attacks.
"Terrorism has no respect for human life and no regard for our laws - this is not the time for circular arguments about jurisdiction or terminology," he will say.
A war of words is playing out between the immigration minister and Labor on proposed changes to Australia's citizenship laws.
Peter Dutton plans on introducing legislation to parliament this week which introduces a values test and tougher English language requirements.
The minister has also revealed the legislation will give him the power to overturn citizenship decisions by the Administrative Appeals Tribunal, as he can already do on some visa matters.
But Labor's citizenship spokesman Tony Burke says those details were not explained during a briefing with Mr Dutton on May 8.
"That's all new," Mr Burke told reporters in Canberra on Tuesday.
He says the government is unable to estimate how many people will pass the tougher English test.
