Mr Abdel Ghani, also Iraq's Deputy Prime Minister, led a delegation on Sunday to Erbil, the capital of the Kurdistan region, to push on the process of finalising a deal to resume the oil exports which have been shut down since March.
Then, Turkey halted the flow of oil produced in the region after an arbitration court ruled in favour of Baghdad, saying Ankara had breached a 1973 agreement when it allowed Iraqi Kurdish authorities to pump and export oil without Baghdad's consent.
The ruling by the International Chamber of Commerce in Paris stopped about 450,000 barrels per day from being exported from Kurdistan and oilfields in northern Kirkuk.
The court ordered Ankara to pay Baghdad damages of about $1.5 billion for unauthorised exports by the Kurdistan Regional Government between 2014 and 2018.
No oil from the region has since been exported.
“The Prime Minister reaffirmed the KRG's readiness to resume oil exports,” the Kurdistan Regional Government said in a statement after Sunday's meeting, with the talks set to continue on Monday.
The KRG emphasised the importance of “mutual understanding regarding the technical and financial aspects of the process”.
Mr Barzani “stressed the need to uphold the constitution and mutual agreements to protect the rights of all parties and address the Kurdistan Region's interests in oil production and transportation cost recovery”, the KRG added.
Shortly after his arrival in Erbil on Sunday, Mr Abdel Ghani said he expected to reach agreement with Kurdish authorities and foreign oil companies to resume crude production within three days.
The Director General of Iraq's State Organisation for Marketing of Oil (Somo) as well as other federal officials are part of Mr Abdel Ghani's delegation.
The KRG had said Iraq's 2005 constitution gave it the right to sign agreements with oil companies and states without consulting Baghdad. But Baghdad maintained the region had no right to sign deals and said exports had to go through state-run pipelines and be marketed by Somo.
One of the thorny issues is the status of oil contracts signed by the KRG, which Baghdad has long considered to be in breach of the country's constitution as they allow oil companies a share in Iraqi oil, which “belongs to the Iraqi people," according to the 2005 constitution.
On Wednesday, representatives from the Iraqi Oil Ministry met several international oil companies in Dubai, according to the Association of the Petroleum Industry of Kurdistan (Apikur), which includes a number of companies operating in Kurdistan.
In that meeting, the companies proposed to sell their share in oil to the federal government, Apikur said in a statement after the meeting.
“As the most expedient way to resume exports through the Iraq-Turkey Pipeline (ITP), Apikur proposed that Somo negotiate crude oil purchase/sale contracts with Apikur members,” said the statement.
Apikur representatives told Baghdad its members “will be able to resume full oil production when there is a clear, well-defined, legally-binding agreement on oil sales and export terms, including payments for past and future sales".