He's also shocked by Senator Anning's call in his first speech for a "final solution" to the immigration problem, which invoked the rhetoric used by Nazi leaders in their massacre of six million Jews.

"Senator Anning's remarks are appalling, I condemn them and I reject them in their entirety," Mr Turnbull told reporters on Wednesday.

The ex-One Nation senator linked Muslim communities to terrorism, and called for an end to Muslim migration, in his speech on Tuesday night.

Mr Turnbull said he spoke as a prime minister whose solemn responsibility was to keep Australians safe when he rejected Katter Senator Anning's comments.

"Those who try to demonise Muslims because of the crimes of a tiny minority are only helping the terrorists," Mr Turnbull later said in parliament.

He was speaking on a Labor motion mirroring former prime minister Bob Hawke's 1988 motion about Australia's non-discriminatory immigration policy.

Mr Turnbull and Opposition Leader Bill Shorten shook hands across the despatch box after their speeches condemning Senator Anning.

Senator Anning also praised the White Australia policy, which was abolished in 1966.

Mr Turnbull said Australia is the most successful multicultural society in the world, because people of all races and faiths lived in harmony.

"The days of the White Australia policy are long, long ago," he told parliament.

The prime minister said the reference to the "final solution" was a shocking insult to the many survivors and families of those who died in the Holocaust.

Australian Associated Press