The UN investigation also makes recommendations on 14 other areas in northern Iraq that have been contested by political and ethnic communities.
De Mistura said on Wednesday: "We are all too aware that tensions have recently risen in parts of the disputed areas... We are hoping that sustained and serious dialogue will now follow."
The response to the report from Talabani, Maliki, and Barzani was "broadly positive" when de Mistura briefed them in advance of the document's handover, a UN official said on condition of anonymity.
A political agreement from the concerned Iraqi parties on each point of the report is required before a referendum on the issues can be held.
"If we thought we were going to inflame the situation still further by doing so, we wouldn't have submitted these reports," the UN official said.
Following the removal from power of Saddam Hussein, a Sunni Arab, by the US-led invasion of Iraq in 2003, Kurds won control of the provincial government.
Thousands of Kurds and Turkmen who had been forced out of the province in favour of southern Arabs during Saddam's rule have since returned to the region.
Kurds say that Kirkuk belongs to their mainly autonomous northern region, but Turkmen and Arab leaders are opposed to such a scenario.
Maliki's recent efforts to send more Iraqi forces to Kirkuk has prompted unease among Kurdish Peshmerga troops stationed there.
Highlighting the tense atmosphere in the province, the number of US forces in Kirkuk has more than doubled since the beginning of this year, with American troops brokering between rival Iraqi groups.