Mr Shorten said he had tried to explain what had happened to his children but there was "no good explanation for this."
“Not all right-wing extremist hate speech ends in violence, but all right-wing extremist violence started in hate speech,” Mr Shorten said at the Islamic Council of Victoria in Melbourne.
The alleged attacker, 28-year old NSW man Brenton Tarrant, live-streamed the murders on Friday and posted a manifesto online steeped in fascism and white supremacism.
"It was an Australian who did this," said Mr Shorten. "This is not an Australian who represents Australia. This is not who we are - but that is why solidarity is so important."
Tarrant was not on the watchlist of either New Zealand or Australian authorities, raising questions about how he flew under the radar of police while being active on online message boards.
Mr Morrison said the views of white supremacists "were not new" and "sadly had existed in Australia for hundreds of years".
"Hatred, bigotry, racism, these are things that we do stand against and we always seek to combat. We are a tolerant, multicultural society, the most successful immigrant country on the planet," he said.
An hour after Mr Morrison spoke, conservative independent senator Fraser Anning addressed a far-right rally of 100 supporters in Melbourne's south-east, restating his belief that Muslim immigration was to blame for the Christchurch shooting.
"Muslims are the people who destroyed 52 other countries around the world," he said, without offering any evidence to back up his claim.
A bipartisan censure of Senator Anning will be moved by the Coalition and Labor when Parliament resumes in April, condemning him for his comments and a statement he put out within hours of the attack.
A censure is an expression of the Senate's disapproval of actions taken by a member of Parliament, but has no direct constitutional or legal consequences.
Mr Morrison said Senator Anning should be “ashamed of himself".
He said he wouldn't normally give "any oxygen" to the comments but he wanted to make it clear that he "absolutely and completely denounced the statements".
"These comments are ugly, they are appalling, and they have no place in Australia or in the Australian parliament," he said.