Syrian troops have begun sweeping into Kurdish-held territory on a collision course with Turkish forces and their allies, a day after the beleaguered Kurds agreed to hand over key cities to Damascus in exchange for protection.

The deal, which Kurdish leaders emphasised they had made reluctantly after four days of bombardment by Turkish artillery and jets, threatens to open a new front in Syria’s nearly nine-year civil war, and signals the likely end of US and European military deployments in the country’s north-east.

There were several flashpoints across north-eastern Syria on Monday. Syrian rebel groups loyal to Ankara launched an assault on the Kurdish-held city of Manbij with support from Turkish artillery and an air strike, a rebel commander told the Guardian. The militiamen – including many fighters who hailed from the city and fled years ago – clashed not only with Kurdish fighters but Syrian regime troops, fighting together for the first time since Sunday’s deal.

US troops were understood to still be on the ground in pockets of north-east Syria, including al-Saediya village, about 4 miles (7km) west of Manbij. US armoured vehicles were also stationed on a bridge into Kobane, sources said, trying to deter the Syrian regime’s entry into the city where Kurds and the US cooperated to inflict Islamic State’s first major defeat in 2015.

Further to the east, the Syrian army said it had reached the town of Tal Tamr, bringing it to within 20 miles of the Turkish border. Syrian state television on Monday afternoon showed government soldiers entering the town of Ain Issa, about 21 miles away from the border.

Unconfirmed reports said Syrian army troops had clashed overnight with Kurdish fighters in the city of Qamishli, which was not surrendered to Damascus in Sunday’s Russian-brokered agreement. The final terms of the deal appeared to still be under discussion on Monday, with several contradictory reports of its contents emerging.

Meanwhile, Turkish fighters and their allies were continuing to attack Tel Abyad and Ras al-Ayn, two cities that have been the focus of Ankara’s mission to push Kurdish fighters – whom it considers to be terrorists – away from its southern border and create a 20-mile buffer zone where it says it will resettle at least 1 million Syrian refugees.

In a statement, the European Union said it unanimously condemned Turkey’s offensive and asked all member states to stop selling arms to Ankara.

Syria and Turkey have exchanged hostilities sporadically throughout the past nine years but their forces have never engaged in sustained combat, pulling back from doing so at key moments in earlier Turkish incursions into Syrian territory.

The prospect of fighting between Syrian troops and Turkish soldiers and their allies raised deep concerns over the security of the estimated 11,000 Isis fighters and their families who are detained across the region. At least 750 people with links to the terrorist group escaped from detention camps in the area on Sunday.

Play Video 4:04 What does Turkey's military action in northern Syria mean? – video explainer

Syrian state media said on Monday that units from President Bashar al-Assad’s army were moving north to “confront Turkish aggression on Syrian territory”.

“After everything, it seems that the fate of the Kurdish people [is to be abandoned],” Ismat Sheikh Hassan, the leader of the military council in Kobane, told local television. “We did everything that we could, we called upon the international community … but it did not result in a solution. We urged all Kurdish [groups] to show solidarity, but no one listened.”

The deal is likely to bring a bitter end to five years of semi-autonomy for Kurdish groups in north-east Syria. Turkey’s Operation Peace Spring started on Wednesday after Donald Trump announced that US forces would withdraw from the region.

Trump had not specified a timeframe for the US withdrawal from Syria, but on Sunday, the US defence secretary, Mark Esper, said the remaining 1,000 special forces had been ordered to leave “as safely and quickly as possible” as the fighting between Turkey and the Kurdish-led Syrian Democratic Forces (SDF) began to threaten US military positions.

The SDF has been funded and trained by the US to combat Isis since 2015, finally defeating the militant group in March after losing 11,000 troops in the battle.

Turkey, however, says the largest unit of of the SDF, the Kurdish YPG, is a terrorist group indistinguishable from the Kurdistan Workers’ party (PKK), which has fought an insurgency against the Turkish state for decades.

Trump’s decision to abandon the SDF to an inevitable Turkish assault has been widely criticised, even by his staunchest allies, as a betrayal that has unleashed a humanitarian disaster and threatens to sow the seeds of an Isis resurgence amid the ensuing chaos.

On Sunday, at least 750 people with suspected links to Isis reportedly fled a displacement camp in north-east Syria. The women and children who were formerly part of the “caliphate” had been held in a secure annexe at the Ain Issa camp. They began to riot and scared away the guards after Turkish shelling struck nearby, said Abdulkader Mwahed, the joint president for humanitarian affairs in the Kurdish-held area of Syria.

The camp was home to about 13,000 people, including three suspected British orphans and a British recruiter for Isis, Tooba Gondal.

Additional reporting by Hussein Akkosh