In a statement, the Egyptian Foreign Ministry asked both sides to avoid more tension that would drag the whole region into instability.
Egypt called on all parties to reach consensus and alleviate tensions that could have negative consequences on the regional and international fronts.
The most populous Arab country stressed the need for maintaining Iraq's unity and territorial integrity and voiced solidarity with all Iraqi people to succeed in facing current challenges.
On Monday, Iraqi security forces fully recaptured the city of Kirkuk and took control of the government building after the Kurdish forces withdrew from the city.
The military operation came after the Iraqi Prime Minister Haider al-Abadi ordered government forces to enter the oil-rich Kirkuk province in northern Iraq to regain control of the disputed areas claimed between Baghdad and the Kurdish semi-autonomous region.
Tensions are escalating between Baghdad and the region of Kurdistan after the Kurds held the September controversial referendum on the independence of the Kurdistan region and the disputed areas.
The independence of Kurdistan is opposed not only by the Iraqi central government, but also by most other countries as it would threaten the integrity of Iraq and undermine the fight against Islamic State militants.
Iraq's neighboring countries, especially Turkey, Iran and Syria, fear that the Iraqi Kurds' pursuit of independence threatens their territorial integrity, as a large Kurdish population lives in those countries.