Government forces have battled their way north for months, notching up key victories against IS, but Tikrit has been their toughest target yet with the jihadists having resisted them several times.
Commanders voiced hope the broadest operation since IS overran swathes of the country last year would be a step towards the liberation of Mosul, the jihadists' main hub in Iraq.
"Security forces are advancing on three main fronts towards Tikrit, Ad-Dawr (to the south) and Al-Alam (to the north)," a senior army officer on the ground told AFP by telephone.
The army officer said the forces involved were from the army, police, counter-terrorism units, a government-controlled volunteer group known as the Popular Mobilisation units and Sunni tribes.
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Military sources said warplanes were involved but it was not immediately clear whether foreign air support -- Iranian or from the US-led coalition fighting IS -- was also called in.
Both Iraqi and Iranian media said Qassem Soleimani -- the commander of the Al-Quds Force covert operations unit of Tehran's elite Revolutionary Guards -- was in Salaheddin province to help coordinate operations.
Hadi al-Ameri, the Popular Mobilisation units' powerful commander, on Saturday urged Tikrit residents to leave their homes within 48 hours so government forces could "wrap up the battle of the revenge for Speicher".
Speicher is a military base near Tikrit from which hundreds of new, mostly Shiite, recruits were kidnapped before being murdered execution-style in the early days of the IS offensive that swept through much of the Sunni Arab heartland north and west of Baghdad in June.
Some Sunni tribes have been accused of direct involvement in the Speicher massacre.
Abadi appealed to residents to turn against the jihadists, who have suffered a string of losses since Iraq's foreign partners stepped up their support.