Turkey on Monday blasted an agreement between Kurdish-led forces in Syria's northeast and a US oil company as "unacceptable" and equivalent to terrorism financing.

Senior Washington officials have confirmed that a US oil company has signed an agreement with the Syrian Democratic Forces (SDF) to "modernise" oil fields under its control. Syria already condemned the deal as "theft" and an "affront to (its) national sovereignty" on Sunday.

The SDF is a Kurdish-led paramilitary alliance that backs a semi-autonomous administration in northeastern Syria and controls the country's biggest oilfields. The US-backed SDF is mostly made up of Syrian Kurdish militia forces which Turkey considers to be a "terror group" linked to the outlawed Kurdistan Workers' Party (PKK).

The Turkish foreign ministry said the name of the US company was Delta Crescent Energy LLC, according to press reports. "We regret the US support for this step that ignores international law and that targets Syria's territorial integrity and sovereignty," the ministry said in a statement.

It considered the deal to be "the financing of terrorism" and "unacceptable."

The foreign ministry accused Syrian Kurdish militia force of advancing "its separatist agenda by confiscating, with this step, Syrian people's natural resources."

"Syria's natural resources belong to Syrian people," it added.

US Senator Lindsey Graham, a longtime supporter of the Syrian Kurds, told Congress on Thursday that he had spoken to SDF commander General Mazloum Abdi about the deal. Asked by Graham if the US was supportive of the deal, Secretary of State Mike Pompeo said: "We are."

The US support for YPG in Syria has become one of the stumbling blocks in bilateral ties between the two NATO allies. The Turkish military has launched three incursions into Syria to fight Islamic State jihadists and the Syrian Kurdish militia force, which has been a crucial American ally in the fight against IS extremists.