Turkey's military offensive in the majority Kurdish enclave of Afrin in northern Syria could take many months rather than the few weeks originally planned, according to commanders on the ground.

Seven Turkish soldiers were killed on Saturday in attacks by Kurdish militias, making it the single deadliest day in the Afrin campaign so far for Ankara.

The deaths highlighted the challenges facing the military as it seeks to oust the Kurdish militias from its border with Syria, and the brewing geopolitical battle with the United States, a Nato ally, which had armed the same militias Turkey is now fighting.

"They will pay for this twice as much," Prime Minister Binali Yildirim said on Twitter, referring to the militants that had killed Turkish soldiers. "We instantly gave the necessary response, and we continue to do so."

Turkey launched Operation Olive Branch, an incursion spearheaded on the ground by Syrian rebels backed by Ankara, two weeks ago.

The area is controlled by the Democratic Union Party (PYD) and its military wing, the People’s Protection Units (YPG). The two groups are backed by the United States-led coalition against ISIL, which relied on their fighters on the ground to oust the terror group from its strongholds in Syria, including the city of Raqqa.

But the PYD and YPG are also the Syrian wing of the Kurdistan Workers’ Party (PKK), a designated terror group that has fought a decades-long insurgency against the Turkish state.

Initial statements by top Turkish officials had asserted the campaign would be concluded in a short time, but limited gains on the ground due to what they say is an attempt to limit civilian casualties mean it now appears it may take months to resolve.

"If you’re optimistic," said one Turkish-aligned rebel fighter taking part in the campaign, when asked if the operation could take six months. He said the YPG fighters had fought fiercely in the initial phase of the battles and had prepared effective defensive lines.

Turkish officials also say US policy in Syria now risks prolonging the war.

Ankara for years tolerated Washington's reliance on the Kurdish militias in the campaign against ISIL but after the group’s defeat in Syria has grown increasingly vocal in demanding an end to American military support for them. The immediate cause of the Afrin campaign was an American announcement that it would create a 30,000-strong border force to patrol Syria’s frontiers including the YPG, a prospect that Turkey decided was an intolerable security threat.

"We are urging our American allies to stop supporting YPG and PYD because now as they say Daesh [ISIL] threat has been eliminated in Syria," said Ibrahim Kalin, the spokesman for Turkish President Recep Tayyip Erdogan, at a briefing in Istanbul. "For the last two years they told us and everyone that they support PYD because of the Daesh threat and now Daesh is over, but they still continue to support them militarily [and] politically."

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Turkey's row with the US over its support for Kurdish militias has raised questions over Washington’s long-term plans for Syria and its presence there, which has expanded on the ground despite the declared military defeat of ISIL in both Iraq and Syria.

Secretary of State Rex Tillerson gave a broad outline of the Trump administration's Syria strategy last month, indicating the government's support for a long-term presence that would prevent the re-emergence of ISIL and counter-balance Iran’s growing influence in both Syria and Iraq through its proxy militias fighting on the ground.

But those plans have alarmed critics who argue the US is setting the stage for a continued proxy war in Syria that makes a political settlement less likely, and who worry that its continued reliance on the Kurdish militias will create an effective autonomous zone with American security guarantees.

Those concerns have further exacerbated tensions between the US and Turkey, two Nato allies whose relations have deeply suffered because of Syria.

"What they see is that Iran is going to stay in Syria in the long run," said a senior Turkish official. "This idea, supported by the Americans, Saudis and Israelis, [is] that there should be some counter-force against the Iranian presence in Syria.

"This kind of Iran, Iran, Iran emphasis or obsession drives them into this kind of policy, and Syrian territories are just becoming a scene for this proxy war now," the official added.