Ashton said that the suspects were "self-radicalized" but inspired by Islamic State ideals.
Police believed the threat had been neutralized through the raids on five Melbourne premises, he said.
Police had been monitoring the men for a long time but stepped up efforts in the last two weeks as it appeared something was going on.
Police and security services in Australia say that they have foiled a Christmas Day terror attack that had been planned against Melbourne's Anglican Cathedral.
One of the suspect's brothers, who named himself only as Ahmed, said around 30 officers in riot gear stormed his home in Gladstone Park, in north west Melbourne.
Prime Minister Malcolm Turnbull has praised counter-terrorism police for foiling an "Islamist terrorist plot" planning to target iconic Melbourne locations on Christmas Day.
"We do believe. that we have removed this threat in its entirety".
Five individuals are in custody after Australian police thwarted an attempted Christmas Day bombing.
The State Police Chief Commissioner told reporters all seven are followers of the Islamic State.
Turnbull said the attack was aimed at disrupting festivities ahead of Christmas and New Year.
Of those seven people, five are still in custody and being questioned.
Graham Ashton says if it had gone ahead, it would have been a significant attack.
"This was not an act of faith, it was not an act of religious observance, it was instead an act of evil... a criminal act", Mr Andrews said.
Victoria Police claim the group had been planning an "ISIS-inspired explosive event" which could have killed or injured a "substantial" number of people in the next few days.
Commissioner Ashton confirmed that police executing the warrants had "gathered the makings of an improvised explosive device".
These terrorists seek to turn us on each other in what should be a time of peace.
Victoria Premier Daniel Andrews denounced the plot as a crime rather than an expression of religion, and called Victoria's multiculturalism a strength.