They say intervention is needed to ensure oil continues to flow from the north of Iraq to Turkey to prevent Turkey having to increase oil shipments from Iran and Russia.
They also say the economy of the Kurdistan region (KRI) could be at risk of collapse if it loses oil revenues.
Relations soured in February when Iraq's federal court deemed an oil and gas law regulating the oil industry in Iraqi Kurdistan was unconstitutional.
Following the ruling, Iraq’s federal government, which has long opposed allowing the Kurdistan regional government (KRG) to independently export oil, has increased its efforts to control export revenues from Erbil, the capital of the KRI.
Before the ruling, Dallas-based HKN Energy wrote to U.S. ambassadors in Baghdad and Ankara in January seeking mediation in a separate case dating back to 2014 concerning the Iraq-Turkey pipeline (ITP), a copy of the letter seen by Reuters shows.
Baghdad claims that Turkey violated the ITP agreement by allowing KRG exports - it deems illegal – through the pipeline to the Turkish port of Ceyhan.
Turkey's energy ministry did not respond to a request for comment.
The final hearing from the case took place in Paris in July, and the International Chamber of Commerce will issue a final decision in the coming months, Iraq's oil ministry said.
Turkey's next steps remain unclear should the court rule in Iraq’s favour, an outcome considered likely, according to three sources directly involved.
At least one other oil firm has engaged at senior levels with four direct and indirect stakeholder governments to encourage engagement, a representative from the company told Reuters, on condition of anonymity.
Other operators in the KRI, Genel Energy (GENL.L) and Chevron , declined to comment on the arbitration case, while DNO and Gulf Keystone did not immediately respond to a request for comment.
Apart from requiring Turkey to get more crude from Iran and Russia, a cessation of oil flows through the ITP, would cause the KRI's economy to collapse, HKN's letter to U.S. representatives said.
Neither the KRG's ministry of natural resources nor the oil ministry in Baghdad responded to a request for comment.
Already Iraq is getting less than the full benefit of high oil prices , which leapt to 14-year-highs after major oil exporter Russia invaded Ukraine in February and they remain close to $100 a barrel.
The ITP has the capacity to pump up to 900,000 barrels per day (bpd) of crude, roughly 1% of daily world oil demand, from state-owned oil marketer SOMO as well as the KRG.
For now it is pumping 500,000 bpd from northern Iraqi fields, which will struggle to boost production further without new investment.
Analysts have said companies will withdraw from the Kurdistan region unless the environment improves.
Already many foreign companies have lost interest.
They first came to Kurdistan in the era of former Iraqi President Saddam Hussein, when the region was considered more stable and secure than the rest of Iraq.
As security has deteriorated, the handful of mostly small and medium-sized firms left has also sought U.S. engagement to help deter attacks against energy infrastructure and improve security generally.
The firms gave their backing to letters written from U.S. congress members to Secretary of State Antony Blinken sent in August, according to sources directly involved in the matter. They asked not to be named because of the sensitivity of the issue.
The letters urged high-level engagement with Erbil and Baghdad to safeguard the stability of the KRI’s economy and to ensure Iraq is free from Iranian interference.
State Department spokesperson Ned Price said on Aug. 16 that disputes between Baghdad and Erbil were between the two sides, but the United States could encourage dialogue.
The State Department summoned U.S. law firm Vinson & Elkins, which is representing Iraq’s oil ministry in Baghdad, for a briefing in Washington on the ITP dispute in July.
A further two briefings are likely to take place in Baghdad and Washington, according to a source familiar with the matter.
"Baghdad would certainly welcome U.S. statements to the KRG leadership that it should follow the Iraqi constitutional arrangements for the oil industry in Iraq," partner at Vinson & Elkins James Loftis said.
The U.S. state department declined to comment but industry experts believe U.S. intervention is unlikely and in any case might not help.
"The U.S. has become disengaged from Iraq over the past decade. No pressure from Washington or other governments will resolve the issues between Baghdad and the Kurds," Raad Alkadiri, managing director for energy, climate, and sustainability at Eurasia Group.
A Kurdish official told Reuters in August the KRG had asked the United States to increase their defence capabilities, but said it was not hopeful as the United States' higher priority is reviving the 2015 nuclear deal with Iran.