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 operation would be a step towards the recapture of Mosul, the jihadists' main hub in Iraq.
The operation began early Monday morning after being announced by Prime Minister Haider al-Abadi the previous evening.
Military sources said warplanes were involved, but the Pentagon said they excluded those of the US-led coalition fighting IS.
"We're not providing air strikes in support of the operation around Tikrit," said Pentagon spokesman Colonel Steven Warren.
It was unclear whether Iranian planes were involved, however.
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 co-ordinate operations.
Abadi urged the security forces to spare civilians, a message echoed by the UN and responding to fears of reprisals against Sunnis in the area.
Tikrit is the hometown of executed dictator Saddam Hussein, the remnants of whose Baath party have collaborated with IS in attempting to topple the Shi'ite-dominated government.
IS declared a caliphate in June straddling Iraq and Syria, where the US-led coalition has also been conducting air strikes but not coordinating with any significant ground force.
A senior US senator said American forces were specifically targeting Mohammed Emwazi, the London man dubbed "Jihadi John" believed responsible for videotaped executions of US and other Western hostages in Syria.
"Oh, yes. He's a target. There should be no question about that," former Senate Intelligence Committee chair Dianne Feinstein said.
IS 'executes four Iraqis from Tikrit'
The Islamic State jihadist group has released a video in which four Sunni tribesmen from the Tikrit region are executed for allegedly collaborating with the government.
The video describes those executed as belonging to a tribal group named after a town just north of Tikrit.
"Elimination of a Sahwat al-Alam cell," reads a banner just before masked gunmen are seen shooting a bullet into the back of each victim's head.
ISIS released pictures of the execution of 13 alleged members of the group in December.
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