Gunman Yacqub Khayre, 29, was killed by police in Melbourne's suburb of Brighton Monday during the two-hour siege in which he also took a woman hostage.
Victoria State Premier Daniel Andrews told Sky News television that the raids were conducted "in connection with the terrible tragic events of Monday in Brighton."
Police in a statement said authorities were conducting a police operation they did not describe in detail in Melbourne's northern suburbs.
The Islamic State group claimed responsibility for the violence.
Khayre, a Somali-born refugee, was acquitted by a Sydney court in 2005 of plotting a suicide attack at an army base a year earlier.
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