Fighting was continuing on the border between Syria and Turkey on Friday in defiance of a supposed five-day ceasefire negotiated between the US and Turkey, amid allegations of war crimes.

Intermittent artillery fire and ground clashes were heard in the border town of Ras al-Ayn on Friday morning, one of the two main targets of the nine-day-old Turkish offensive, as the Turkish military and Syrian rebel proxies struggled to wrest control of the town from the Kurdish-led Syrian Democratic Forces (SDF).

Kurdish officials said the hospital at Ras al-Ayn had been shelled, and it was impossible to evacuate the wounded because the town was surrounded. A statement by the SDF’s political wing, the Syrian Democratic Council, said Turkey and its proxies had ignored the ceasefire, and it appealed for international monitors to be placed in the region.

Amnesty International said it had compiled “damning evidence” of crimes committed by Turkish forces and Syrian militias backed by Ankara. Amnesty claimed they displayed “a shameful disregard for civilian life, including through summary killings and unlawful attacks that have killed and injured civilians”.

At the same time, UN chemical weapons inspectors launched an investigation following accusations that burning white phosphorus was used by Turkish forces against children in Syria earlier this week.

The fighting showed no signs of abating a day after a US delegation led by the vice-president, Mike Pence, announced they had agreed a ceasefire with the Turkish president, Recep Tayyip Erdoğan, in Ankara – a deal the US president, Donald Trump, claimed was “a great day for civilisation” that would save “millions of lives”.

On Friday, Trump played down the violations, saying he had received personal reassurance from Erdoğan, and that the “ultimate solution”, supposedly of a peace deal, would be achieved.

“He told me there was minor sniper and mortar fire that was quickly eliminated,” Trump tweeted. “He very much wants the ceasefire, or pause, to work. Likewise, the Kurds want it, and the ultimate solution, to happen.”

The US president then retweeted a statement from Erdoğan casting the invasion as a counter-terrorism operation. Later in the day, at a teleconference to talk to two American astronauts, Trump made the unexplained claim that “we’ve taken control of the oil in the Middle East … the oil that everybody was worried about”.

It appeared likely that he was referring to oilfields in eastern Syria, that are under SDF control.

In the US, the deal reached in Ankara on Thursday has been strongly criticised by both Democrats and Republicans as a gift to Erdoğan, granting legitimacy to the offensive and suspending sanctions, but requiring no Turkish concessions in return.

The ceasefire was supposed to last for 120 hours but it was unclear from the start whether the SDF had agreed to the terms laid out in Ankara.

However, while the SDF commander, Mazloum Kobane, acknowledged the ceasefire, he said his fighters were ready to abide by it only in the border strip between Ras al-Ayn and Tel Abyad, the other town under Turkish attack.

Quick guide What is happening in north-eastern Syria? Show Hide Who is in control in north-eastern Syria? Until Turkey launched its offensive there on 9 October, the region was controlled by the Syrian Democratic Forces (SDF), which comprises militia groups representing a range of ethnicities, though its backbone is Kurdish. Since the Turkish incursion, the SDF has lost much of its territory and appears to be losing its grip on key cities. On 13 October, Kurdish leaders agreed to allow Syrian regime forces to enter some cities to protect them from being captured by Turkey and its allies. The deal effectively hands over control of huge swathes of the region to Damascus. That leaves north-eastern Syria divided between Syrian regime forces, Syrian opposition militia and their Turkish allies, and areas still held by the SDF – for now. On 17 October Turkish president, Recep Tayyip Erdoğan, agreed with US vice-president Mike Pence, to suspend Ankara’s operation for five days in order to allow Kurdish troops to withdraw. The following week, on 22 October, Erdoğan and his Russian counterpart, Vladimir Putin agreed on the parameters of the proposed Turkish “safe zone” in Syria. How did the SDF come to control the region? Before the SDF was formed in 2015, the Kurds had created their own militias who mobilised during the Syrian civil war to defend Kurdish cities and villages and carve out what they hoped would eventually at least become a semi-autonomous province. In late 2014, the Kurds were struggling to fend off an Islamic State siege of Kobane, a major city under their control. With US support, including arms and airstrikes, the Kurds managed to beat back Isis and went on to win a string of victories against the radical militant group. Along the way the fighters absorbed non-Kurdish groups, changed their name to the SDF and grew to include 60,000 soldiers. Why does Turkey oppose the Kurds? For years, Turkey has watched the growing ties between the US and SDF with alarm. Significant numbers of the Kurds in the SDF were also members of the People’s Protection Units (YPG), an offshoot of the Kurdistan Workers’ party (PKK) that has fought an insurgency against the Turkish state for more than 35 years in which as many as 40,000 people have died. The PKK initially called for independence and now demands greater autonomy for Kurds inside Turkey. Turkey claims the PKK has continued to wage war on the Turkish state, even as it has assisted in the fight against Isis. The PKK is listed as a terrorist group by Turkey, the US, the UK, Nato and others and this has proved awkward for the US and its allies, who have chosen to downplay the SDF’s links to the PKK, preferring to focus on their shared objective of defeating Isis. What are Turkey’s objectives on its southern border? Turkey aims firstly to push the SDF away from its border, creating a 20-mile (32km) buffer zone that would have been jointly patrolled by Turkish and US troops until Trump’s recent announcement that American soldiers would withdraw from the region. Erdoğan has also said he would seek to relocate more than 1 million Syrian refugees in this “safe zone”, both removing them from his country (where their presence has started to create a backlash) and complicating the demographic mix in what he fears could become an autonomous Kurdish state on his border. How would a Turkish incursion impact on Isis? Nearly 11,000 Isis fighters, including almost 2,000 foreigners, and tens of thousands of their wives and children, are being held in detention camps and hastily fortified prisons across north-eastern Syria. SDF leaders have warned they cannot guarantee the security of these prisoners if they are forced to redeploy their forces to the frontlines of a war against Turkey. They also fear Isis could use the chaos of war to mount attacks to free their fighters or reclaim territory.

On 11 October, it was reported that at least five detained Isis fighters had escaped a prison in the region. Two days later, 750 foreign women affiliated to Isis and their children managed to break out of a secure annex in the Ain Issa camp for displaced people, according to SDF officials. It is unclear which detention sites the SDF still controls and the status of the prisoners inside. Michael Safi

The Syrian regime and its Russian allies, who have also moved troops into the contested border zone at the invitation of the SDF, and are not bound by the terms of the US-Turkish agreement, had no immediate comment.

Erdoğan told reporters in Istanbul on Friday he had confirmation that Kurdish fighters were withdrawing, dismissing reports of the ongoing clashes as “speculation, disinformation”. He said Turkish troops would remain in north-east Syria to monitor whether “this terror organisation [is] truly leaving the area”.

The US secretary of state, Mike Pompeo, who visited Turkey with Pence, said the ceasefire would eventually hold.

“There’s not perfect command and control,” Pompeo told Politico. “You have irregular forces in the region, as well. I don’t know precisely what this is, but our sense is, the political commitments that were made yesterday will end up being successful.”

The secretary of state claimed SDF forces were beginning to withdraw from two contested border towns. “So the key elements of the ceasefire look to be taking effect,” he said.

The US position has been met with widespread criticism outside the US too. The chairs of foreign affairs committees in the UK, France, Germany, the EU and the US House of Representatives issued a rare joint statement condemning Turkey’s invasion into Syria as military aggression and a violation of international law. The joint statement also rejected Trump’s decision to abandon the Syrian Kurds, saying it was likely to lead to a resurgence of Islamic terrorism.

The EU council president, Donald Tusk, said the “so-called” ceasefire was in fact “a demand of capitulation of the Kurds”, while the French president, Emmanuel Macron, described Turkey’s incursion as “madness”. Macron added that he expected to meet Erdoğan alongside Boris Johnson and Angela Merkel in London in the coming weeks.

Turkey launched Operation Peace Spring, aimed at driving the SDF away from its border, on 9 October. The assault was triggered by Trump’s announcement that US troops would withdraw from the region, which removed the buffer that had stopped Turkey attacking the Kurdish-led force.

On Thursday it emerged that Trump had sent his Turkish counterpart a bizarre letter warning him “don’t be a fool” and saying history risked branding him a “devil” . Erdoğan responded on Friday by saying his country “cannot forget” the letter but that the mutual “love and respect” between the two leaders prevented him from keeping it on Turkey’s agenda.

Ankara maintains the SDF is indistinguishable from Turkey’s outlawed militant Kurdistan Workers’ party (PKK) and has long been angered by US support for the group during the five-year-long campaign to defeat Islamic State.

The offensive has been widely condemned for triggering a humanitarian crisis and risking the re-emergence of Isis amid the chaos. At least 300,000 people have fled their homes in the fighting and at least 71 people have been killed in north-east Syria, according to the UN and a human rights monitor. Over the border in Turkey, 20 civilians have been killed in counterattacks.

Play Video 1:13 Mike Pence: US and Turkey have agreed to a ceasefire in Syria – video

A statement released by Washington and Ankara after the ceasefire talks did not define any changes to the size and scope of Turkey’s proposed safe zone, which Turkish officials have previously said should be 20 miles deep and stretch 270 miles from the contested town of Manbij to the Iraqi border.

The statement also reiterated the US understanding of Turkey’s need for a safe zone, which would be “primarily enforced by the Turkish armed forces” after the Kurdish withdrawal, implying that Ankara still intends to occupy the entire area.

Erdoğan is due to meet his Russian counterpart, Vladimir Putin, in Sochi on Tuesday, where it is expected further concrete talks on the size of Turkey’s planned buffer zone will take place.