He said he had information that more terror attacks were being planned inside and outside Chechen territory.
As he spoke, nine Russian servicemen died on board a military helicopter that crashed in Chechnya.
According to the Russian military, the Mi-8 helicopter was shot down by rebels who launched a rocket from a building on the outskirts of Grozny.
This is the second helicopter lost by the Russian army in less than a week.
On Tuesday another Mi-8 was shot down in Chechnya with the loss of four lives.
'Tough and targeted'
Mr Ivanov also said that previous plans to reduce the Russian military presence in Chechnya had been suspended.
The offensive comes a week after Russian troops stormed a Moscow theatre in which about 800 theatre-goers were taken hostage by Chechen rebels.
One-hundred-and-nineteen hostages died in the siege and subsequent assault by Russian forces, as well as about 50 rebels.
Russian news agency Itar-Tass quoted Mr Ivanov as saying that the operations launched on Saturday were aimed at "nipping the threat in the bud".
"In the past few days we have received more and more information that on the territory of Chechnya, and not only there, guerrilla fighters are preparing to carry out new acts of terror," he said.
The military actions, the Interfax news agency quoted Mr Ivanov as saying, are "broad-scale, tough and targeted".
On Friday Mr Ivanov had insisted that the planned troop withdrawal from Chechnya would continue despite the hostage crisis in Moscow.
Russian authorities have imposed tough restrictions on reporting from Chechnya and access there by Russian and foreign correspondents is under strong Kremlin control.