The Turkish government has claimed that Donald Trump has handed it the leadership of the military campaign against Isis, and warned its forces would be crossing into Syria “shortly”.

Kurdish military leaders inside Syria said they were braced for the invasion and claimed there had been an Isis attack on its former stronghold of Raqqa. But reports from the city suggested the attack had been small scale.

However, it deepened Kurdish fears they would soon find themselves fighting on several fronts, against Turkey, Isis and possibly Iranian or Russian-backed units aligned with Damascus, all without US support.

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A spokesman for the Turkish president, Recep Tayyip Erdoğan, justified the impending invasion by saying that Trump, in a telephone conversation with Erdoğan on Sunday, had handed Turkey the mantle of the counter-Isis battle that the US has been waging alongside Kurdish forces since late 2014.

Fahrettin Altun, Erdoğan’s communications director and one of his closest aides, suggested Trump had given the Turkish leader the green light for an invasion, contradicting denials from White House officials.

“During a phone call with President Recep Tayyip Erdoğan on Sunday, President Trump agreed to transfer the leadership of the counter-Islamic State campaign to Turkey,” Altun wrote in a commentary in the Washington Post published on Tuesday evening. “The Turkish military, together with the Free Syrian Army, will cross the Turkish-Syrian border shortly.”

Brett McGurk (@brett_mcgurk) This is not a surprise. The POTUS green-lighting a Turkish attack into NE Syria (that's how it's seen by all parties on the ground and in the region) opens Pandora's box. Expect Russian-backed forces to move as well. Total mess. https://t.co/DycWpDn7RD



Altun also suggested that the Turkish operation could be far more extensive than the 32km-deep border safe zone that US and Turkish officials had been working together to establish before Erdogan announced the planned assault.

The southern border of the safe zone could reach as far as Deir Ezzor and Raqqa provinces, he said, effectively signalling Turkey could seek to take over the entire area currently controlled by the Syrian Democratic Forces (SDF).

In his address to the UN General Assembly last month Erdoğan had floated an expanded zone as means to resettle Syrian refugees in Turkey, saying it could hold as 3 million people.

Altun portrayed the invasion as a counter-terrorism operation, and described Kurdish forces in north-eastern Syria, the YPG, as “armed thugs” who should not resist the Turkish takeover of the area.

“It remains to be seen whether YPG militants will agree to the change in the campaign’s leadership,” he wrote. He added in a later tweet: “YPG militants have two options: They can defect or we will have stop them from disrupting our counter-Isis efforts.”

The Syrian Democratic Forces said late on Tuesday night that Turkish forces were already attacking near the border. “The Turkish military is shelling one of our points on SereKaniye Border with Turkey,” it said in a tweet, referencing the key border town of Ras al-Ayn.

It was one of the places from which US troops withdrew on Monday, according to the UK-based Syrian Observatory for Human Rights.

“There were no injuries to our forces. We didn’t respond to this unprovoked attack,” the SDF said.

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Early on Monday, US special forces near the Syrian-Turkish border were ordered to withdraw from their posts, to the surprise of Americans and Kurdish commanders. The Pentagon said on Tuesday the redeployment was necessary to avoid US troops being caught in the crossfire.

“Unfortunately, Turkey has chosen to act unilaterally,” Jonathan Hoffman, chief Pentagon spokesman, said. “As a result we have moved the US forces in northern Syria out of the path of potential Turkish incursion to ensure their safety. We have made no changes to our force presence in Syria at this time.”

There are also British and French special forces in the region and in the event of a major Turkish-Kurdish conflict the Guardian understands they would be tasked with the bolstering the security of camps where captured Isis fighters are being guarded by the Kurds.

“We are nervous, and very much against this Turkish offensive,” a European official said on Tuesday. The official expressed hoped that the offensive could be limited in scope and not trigger a full-scale conflict with the YPG (and its broader coalition, the SDF), that could lead to the scattering of Isis prisoners and the movement’s resurgence.

“If it is an unmitigated Turkish offensive, we are going to suffer serious consequences,” the official said.

Military analysts warn of the possibility of a multi-pronged attack on Kurdish-held areas, with Turkey advancing from the north, and militias aligned with the Damascus regime, supported by Iran and Russia striking from the south.

“Russia and Turkey have already discussed Turkey’s upcoming operation,” Jennifer Cafarella, research director at the Institute for the Study of War, said. “Russia supports it at least tacitly and may actually have entered into a general agreement with Turkey on the shape of what is to come in the north-east.”

Joseph Votel, who headed US central command until March and was instrumental in establishing the partnership with the Kurds, said the abrupt policy decision to seemingly abandon Washington’s Kurdish partners could not have come at a worse time.

In an article he co-wrote on the Defense One military news site Votel said: “This policy abandonment threatens to undo five years’ worth of fighting against Isis and will severely damage American credibility and reliability in any future fights where we need strong allies.”