Egypt's Ministry of Foreign Affairs called on Iraq's central government and the Kurdish regional government to show restraint on Monday as fighters from the two sides clashed in the Kirkuk area.
In a statement, the ministry said Iraqi and Kurdish forces should avoid drifting into confrontations that would fuel tensions and instability in the region, state-run news agency MENA reported.
The ministry called on all parties to engage in dialogue and compromise solutions to defuse a crisis that could have dangerous regional and international implications.
On Monday, Iraqi forces advanced on Kurdish fighters and captured several positions south of Kirkuk in a bid to regain control of the oil-rich city.
The operation was a response to last month's declaration of independence by the Kurdish region following a referendum there.
The Egyptian ministry reaffirmed the need to preserve the territorial integrity of Iraq and the solidarity of the Iraqi people in the face of common challenges.
According to a statement issued by the Iraqi military, the territory captured on Monday includes a key airbase called K1, the North Gas Company facilities, a nearby processing plant, a power plant and the industrial district.
The Kurdistan Regional Government did not confirm the capture of these positions, but major Kurdish TV channel Rudaw said Kurdish Peshmerga forces had retreated from positions south of Kirkuk.
The city of Kirkuk is under Kurdish control but the advance of Iraqi forces to the industrial zone put them in control of its southern access routes.
Iraq launched the operation in the multi-ethnic region early on Sunday, amid an escalating crisis between the Iraqi government and the KRG over the 25 September referendum.