ERBIL, Iraq Iraq's Kurds plan to hold a referendum on independence this year to press their case for "the best deal" on self-determination once Islamic State is defeated, a senior Kurdish official said. The Kurds already run their own autonomous region in northern Iraq and the official, Hoshiyar Zebari, indicated the expected 'yes' outcome in a vote wouldn't mean automatically declaring independence. But with Kurdish forces also controlling wider territory regained from Islamic State, the referendum plan adds to questions about Iraq's unity after the militants have been ousted from Mosul. The two main Kurdish parties, the Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK), agreed at a meeting on Sunday that a referendum should be held this year, Zebari, a senior member of the KDP leadership, told Reuters. "The idea of a referendum has been re-energized," Zebari, a former Iraqi foreign and finance minister, said in an interview in Erbil on Wednesday evening, commenting on the meeting held with the PUK's leadership. The Kurds played a major role in the U.S.-backed campaign to defeat Islamic State, the ultra-hardline Sunni Muslim group that overran about a third of Iraq nearly three years ago. The militants are now fighting off Iraqi forces in Mosul, their last major city stronghold in Iraq from where they declared a "caliphate" that also includes parts of Syria. While the fall of Mosul would effectively end the "caliphate", it will not solve deep divisions over power, land and resources between Iraq's Shi'ite Arab majority, and the important Sunni Arab and Kurdish communities. The two rival Kurdish groups issued a joint statement on Sunday declaring support for the plan of holding a referendum, leaving its exact timing to an agreement with other, smaller Kurdish groups. Zebari described the aim as "self-determination", leaving open the exact nature of any deal with Baghdad following the referendum when Kurds would be likely to vote strongly for independence. "It will give a strong mandate to the Kurdish leadership to engage in talks with Baghdad and the neighbors in order to get the best deal for Kurdish self-determination," he said. Iraqi Kurdish independence has been historically opposed by Iraq and also its neighbors, Iran, Turkey and Syria, as they fear the contagion for their own Kurdish populations. Iraq's Kurds are the community to have advanced the most toward their long-held dream of independence. Iraq has been led by the Shi'ites since the overthrow of Saddam Hussein, a Sunni, in 2003, following a U.S.-led invasion. They run their own affairs in the north, through a Kurdistan Regional Government (KRG), led by KDP leader Massoud Barzani. They have their own armed force, the Peshmerga, which prevented in 2014 Islamic State from capturing the oil region of Kirkuk, after the Iraqi army fled in the face of the militants. The Kurds have historical claims over Kirkuk, which is also inhabited by Turkmen and Arabs. Hardline Iranian-backed Iraqi Shi'ite militias have threatened to expel the Kurds by force from this region and other disputed areas. Kirkuk's Kurdish-led provincial council rejected this week a resolution by the Iraqi parliament in Baghdad to lower Kurdish flags raised since last month next to Iraqi flags over public buildings of the region. Turkish President Tayyip Erdogan also warned the Kurds on Tuesday that failure to lower the Kurdish flags would damage their relations with Turkey. "We don't agree with the claim 'Kirkuk is for the Kurds' at all. Kirkuk is for the Turkmen, Arabs and Kurds, if they are there. Do not enter into a claim that it's yours or the price will be heavy. You will harm dialogue with Turkey," he said at a rally in the Black Sea province of Zonguldak. The KRG government rejected the Iraqi and Turkish demands, arguing that the Kurds' role in defending Kirkuk against Islamic State justified the hoisting of their flag. "If it wasn't for the Peshmerga, there would be neither Iraq's flag in the city nor Kurdistan's," KRG Prime Minister Nechirvan Barzani told reporters in Erbil on Wednesday. Masrour Barzani, head of the KRG's Security Council and son of President Barzani, said in June that Iraq should be divided into three separate entities to prevent further sectarian bloodshed, with a state each given to the Shi'ites, the Sunnis and the Kurds. The Shi'ites live mainly in the south, the Sunnis and the Kurds are on opposite corners of the north while the central region around Baghdad is mixed.