The Iraqi government dismissed a call from U.S. Secretary of State Rex Tillerson for Iranian-backed paramilitary units that helped Baghdad defeat Islamic State and capture the Kurdish-held city of Kirkuk to end operations in Iraq.
The Kurdish offer came after Mr Abadi ordered the Iraqi military to retake disputed territory held by the Kurds.
In a statement released overnight, the Kurdistan government said it would "propose to the government and Iraqi public opinion (.) the freezing of the results of the referendum (.) and the start of an open dialogue between the government of Kurdistan and the central government on the basis of the constitution".
The vote organised by the leadership of autonomous Iraqi Kurdistan in the country's north angered neighbours Turkey and Iran, both fearful of anything that might stoke separatist sentiment among their own large Kurdish minorities.
Baghdad has always considered the Kurdish secession referendum illegal.
Turkey's foreign minister Mevlut Cavusoglu said on Thursday the Kurdish offer to suspend the push for independence was a step in the right direction but did not go far enough.
In addition to a ban imposed by Baghdad last month, barring all global 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. Both contested areas have important oil assets.
Tamil Nadu: Student dies after jumping from school building, two teachers booked
Kollam: A 15-year-old girl, who jumped off from the third floor of a school building here, succumbed to her injuries on Monday. Two teachers of the school - Sindhu and Crescent - have been booked by the Kollam West Police in connection with the incident.
Accusing the USA 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".
Iran's supreme leader, Ayatollah Ali Khamenei, told Iraq's US -backed prime minister on Thursday that he should not rely on the United States in the fight against Islamic State, seeking to drive a wedge between Washington and one of its close allies. "Don't trust America. It will harm you in the future".
Iran remains a major player in the war against the Islamic State group and culturally across Iraq, its one-time bitter enemy when Iraqi dictator Saddam Hussein waged an eight year war on Iran in 1980s that left more than one million casualties on both sides.
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.
"It seems that Barzani admits the defeat of the referendum, and he has realized that Iraq, Iran, Turkey, and even the European Union and US are not happy with him".
"With the referendum they tried to break up our territory, they tried to redefine our borders", Al-Abadi said. Barzani took the helm of the party after his father's death in exile in 1979 and joined his rival, future Iraqi President Jalal Talabani, in splitting control of what would become the Kurdish Regional Government in northern Iraq after the US defeated Iraqi forces in the First Persian Gulf War.