The involvement of Shiite militiamen in the operation, which has been dubbed an attempt to avenge the IS massacre of hundreds of mainly-Shiite recruits last year, has raised fears of sectarian killings targeting Sunni Arabs.
"Military operations in and around Tikrit have precipitated displacement of an estimated 28,000 people to Samarra," the UN said in a statement Thursday.
"Field reports indicate that additional displacements are under way and that yet more families remain stuck at checkpoints," it said.
The newly displaced Iraqis join what the International Organization for Migration says are 2.5 million people already forced from their homes in the country.
Some 30,000 Iraqi security forces members and allied fighters launched the operation to retake Tikrit on Monday, the largest of its kind since IS overran swathes of territory last June.
Retaking Tikrit, the hometown of executed president Saddam Hussein, from militants who have had more than eight months to dig in poses a major challenge for the country's forces.
Sectarian-fuelled revenge killings targeting Sunni Arabs have been a feature of past operations involving Shiite militias, raising concerns that the same may happen in Tikrit.
"We have urged all Iraqi forces to avoid and prevent the abuse to civilians of any kind of activity that violates international norms, fuels sectarian fears, and promotes sectarian divides, and that includes Iran in terms of their activities," US Secretary of State John Kerry said Thursday in the Saudi Arabian capital Riyadh.
Kerry confirmed that the US had information indicating the commander of Iran's powerful Quds force, General Qassem Suleimani, was on the ground in Iraq aiding the offensive.
"We've got information to that effect," he said, insisting however that the operation was Iraqi-led.
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- Ground offensive? -
Speaking at the joint press conference, Saudi Arabia's foreign minister, Prince Saud al-Faisal, urged the US-led coalition conducting air strikes against IS in Syria and Iraq to wage a ground war against the jihadists.
The kingdom, part of that coalition, "stresses the need to provide the military means needed to face this challenge on the ground," he said.
The top Saudi diplomat raised concerns, however, about Iraq's neighbour to the east -- Sunni-dominated Saudi Arabia's arch-rival Iran.
"Tikrit is a prime example of what we are worried about. Iran is taking over the country," Prince Saud said.
The US military's top officer, General Martin Dempsey, said Tuesday that Iran's help in an Iraqi offensive to recapture Tikrit could be "a positive thing," providing it did not fuel added sectarianism.
Before Kerry's confirmation, Suleimani -- the commander of the Al-Quds Force covert operations unit of Tehran's elite Revolutionary Guards -- was already believed to be helping coordinate operations in Salaheddin province.
Dempsey said that "this is the most overt conduct of Iranian support," which came "in the form of artillery" and other aid.
Nickolay Mladenov, the outgoing UN envoy to Iraq, expressed hope for the country's future on Thursday, saying the sectarianism that has plagued it is declining.
"The key change is that now there is hope that Iraq can reconstruct itself in a more inclusive way that allows the country to move forward," Mladenov told AFP.
"It used to be more acceptable to be sectarian, now it's less acceptable to be openly sectarian in your speeches," he said. "This changes the nature of the political environment, slowly but surely."
"I'm optimistic about Iraq yet I'm paranoid that a lot of things can go wrong."