The appeal from the top United Nations body came after Baghdad dismissed an offer from Iraqi Kurdish leaders to freeze the outcome of the referendum, which delivered a resounding yes to independence, and hold talks.
In addition to a ban imposed by Baghdad last month, barring all worldwide carriers from using airports in the Kurdish territory, Turkey has closed its airspace to flights to and from the Iraqi Kurdish region and has said it was considering closing its border to the region as further reprisal.
The three-point text also proposes "an immediate ceasefire and cessation of military operations in Kurdistan", after some 30 Kurdish Peshmerga fighters and members of Iraqi government and paramilitary forces died in operations "to restore central power" in the disputed territories, including the wealthy province of Kirkuk.
The Kurdish Region Security Council released several statements this week accusing Iraqi forces and Iranian-backed Shia Popular Mobilization Units of "multi-pronged attacks" using American-made weapons and vehicles.
Iraq's prime minister has rejected an offer from the Kurdistan Region to "freeze" the result of last month's independence referendum and hold talks. It did not cite the prime minister himself but a "source" close to him.
Turkish President Recep Tayyip Erdogan said on Wednesday that his country is prepared to help Iraq's central government export oil through a pipeline that would largely bypass the Iraqi Kurdish region.
Iraqi authorities did not confirm this account of fighting.
Accusing the U.S. of having created the Islamic State (IS) as a means to "destroy" the Iraqi people and Government, Khamenei warned Abadi "never to trust Americans" as they will "hit Iraq again when they have the opportunity".
"We will preserve Iraq's unity and will never allow any secession", Iran's state news agency IRNA quoted Abadi as saying during his meeting with Khamenei.
Iraqi Kurdish leaders on Wednesday offered to freeze the referendum results in order to facilitate talks with Baghdad and end the violence.
Haider al-Abadi's statement issued early on Thursday says the operation aims to liberate Qaim and Rawa, as well as other villages - the very last remaining strongholds of IS militants in Iraq.
Sporadic clashes have erupted over the past two weeks as Iraqi government forces moved to retake territory that was under federal control before the Islamic State group blitzed across the country in 2014.
The Kurds' referendum last month overwhelmingly backed independence from Baghdad. The KDP was immediately threatened with military action by Iraq and pro-government troops and their allies, including mostly Shiite Muslim militias backed by Iran, have easily retaken a number of towns and oil-rich regions claimed by the country's Arab majority.
Reports of Casualties and Looting Amid ISF, Peshmerga Clashes - On October 20, Human Rights Watch reported that 51 civilians were injured and five killed in Tuz Khurmatu in Salah ad-Din Province during "indiscriminate firing" between Iraqi Security Forces and the Iraqi Kurdish Peshmerga.