The President of the Autonomous Region of Kurdistan Massoud Barzani called on Kurds and Arabs on Friday "to have an open dialogue and find a consensus solution for the city, away from any foreign interventions", dpa reported.
During his few-hours-visit to Kirkuk on Friday, Barzani said: "We do not accept any side imposing its agenda on us, and likewise we do not want to do the same."
The Kurdish leader described Kirkuk as " Iraq's Kurdish city," and asked people to live peacefully together.
"Claiming that Kirkuk is part of Kurdistan does not mean it is not an Iraqi area," Barzani was quoted by the Voices of Iraq news agency as saying.
Barzani's visit comes two days after Iraqi lawmakers failed to agree on the adoption of a controversial new provincial election law affecting the multi-ethnic city.
The bill failed because the sides were unable to come to terms on a power-sharing deal for the oil-rich city that lies some 250 kilometres north-east of Baghdad.
Speaking at a press conference, Barzani told reporters that "he wanted to convey a peaceful message from Kirkuk, an Iraqi and Kurdish city, where people of different ethnic origins have lived together."
During his visit, in which he met with several senior figures including the governor, Barzani said: "We came to Kirkuk in a bid to overcome the crisis and dispel fears that Kurds are trying to seize authority and dominate the province."
The failure in passing a provincial election law is expected to delay Iraq's provincial elections, scheduled for October 1, to at least 2009.
On July 22, Kurds objected to the law that also provides for an equal division in the number of seats in Kirkuk's governorate council, in which the city's population of 1 million Kurds, Arabs and Turkmens would get one-third of the seats representing each group.
Before he left, Barzani visited the families of those people killed during bombings that took place in Kirkuk on July 28. The attack left 22 dead and 150 injured.