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 on Friday.
"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.
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.