Mr Abadi, who is heading a ministerial delegation, left Baghdad for a regional tour, which also includes Iran
Iraq's Abadi visits Turkey for talks on Kurds and oil
Iraqi Kurdistan proposed on Wednesday to freeze the results of its independence referendum and start “an open dialogue” with the central government in Baghdad.
It also called for “an immediate ceasefire and cessation of military operations in Kurdistan”.
There was no immediate reaction from Baghdad – which said the referendum was unconstitutional – but the Iran-backed Popular Mobilisation Units, which played a major role in the operation against the Kurds, said a freeze did not go far enough and demanded the outright annulment of the independence referendum.
Iraqi forces captured the city of Kirkuk from Kurdish fighters on October 16 in response to Kurdistan’s vote on independence.
Two days later, the Iraqi military announced its troops had completed the operation to retake not just Kirkuk city and its lucrative oilfields, but also Kurdish-held areas in Nineveh and Diyala provinces.
The Kurds took control of Kirkuk city in 2014 after the Iraqi army fled a lightning advance by ISIL across north and west Iraq.
Iraqi prime minister Haider Al Abadi met on Wednesday with Turkish president Recep Tayyip Erdogan in Ankara as ties between their two countries have tightened in opposition to the Kurdish vote on independence.
Mr Abadi, who is heading a ministerial delegation, left Baghdad for a regional tour, which also includes Iran.
"There was a plan to dismantle the region and not just Iraq," he said in a statement published on his Facebook page on Wednesday. "They wanted to draw a border in blood and, despite all that, we did not fight our Kurdish people.
"Our orders stressed there be no confrontation and they responded, thank God, with non-aggression. But what is undeniable and unfortunate is the campaign of lies and false accusations that there are non-Iraqi forces in and around Kirkuk."
Tens of thousands of Iraqis heeded a call to arms in 2014 after ISIL seized a third of the country's territory, forming the Popular Mobilisation Units (PMU), which receive funding and training from Tehran and have been declared part of the Iraqi security apparatus.
US secretary of state Rex Tillerson said on Sunday that Iranian-backed Iraqi militias and their Iranian advisers must "go home" now that fight against ISIL is almost over.
Mr Tillerson was in Riyadh for the launch of the Saudi-Iraqi Coordination Council, which aims to promote co-operation between the two countries in the fight against terrorism in the region and in the rebuilding of the Iraqi areas destroyed in the battle against ISIL.
Iraq is looking to Saudi Arabia for economic backing as both oil-dependent economies have suffered from a prolonged price slump.
Adel Al Jubeir, the Saudi Arabian foreign minister, pledged to boost relations with Iraq to a “higher, strategic level” to provide Baghdad with an alternative to pervasive Iranian efforts to exert control over the country.
Meanwhile, Mr Erdogan said that his country was ready and willing to support Baghdad as it seeks to reopen a crude oil pipeline from the Kirkuk oilfields to Turkey, through which Iraq stopped sending oil in 2014.
He added that the two discussed political, military and economic steps they could take after the "illegitimate" Iraqi Kurdish referendum.
Both Iran and Turkey have a sizeable Kurdish population and fear the September independence referendum will encourage their own Kurdish communities to do the same. They have expressed their willingness to work together and with the government of Baghdad, which deemed the vote “illegal”.
Mr Abadi said: “We tried to stop the referendum in Kurdistan but it happened from one side and with no deliberations.”
Mr Abadi’s visit to Ankara comes after relations between the neighbouring countries were strained last year over Turkey's presence at a military base in northern Iraq.
Mr Abadi also met with his Turkish counterpart, Binali Yıldırım, on Wednesday to discuss the latest regional development.
Ankara maintained an estimated 2,000 troops in Iraq, around 500 of them were in the northern Bashiqa camp training local fighters last year ahead of the successful bid to free Mosul from the grip of ISIL.
But since the non-binding independence vote and the countries' mutual vehement opposition to it, Turkey has given its support to Baghdad by threatening to close its border with the Kurdistan Regional Government and apply economic sanctions.
Ankara had particularly criticised the inclusion of Kirkuk in the independence vote, stressing the province's multi-ethnic character, where Kurds, Arabs and Turkmens live.