“There have been significant hostilities in the last two weeks, before a ceasefire was brokered,” Geir Pedersen told the UN Security Council in New York on Tuesday, warning that a military escalation could be “catastrophic”.

The remarks come after the Syrian National Army (SNA), a group of fighters backed by Turkiye, has battled with the Kurdish-led Syrian Democratic Forces (SDF) in the wake of al-Assad’s removal.

The SDF is the main ally in a United States-led coalition against ISIS (ISIL). It is spearheaded by the People’s Protection Units (YPG), which Ankara sees as an extension of the Kurdistan Workers’ Party (PKK) armed group that it outlaws and that has fought the Turkish state for 40 years.

Last week, SNA fighters seized the northern city of Manbij from the SDF, which then headed east of the Euphrates river as a US-mediated ceasefire came into effect.

Meanwhile, the members of the UNSC in a statement called for the implementation of “an inclusive and Syrian-led and Syrian-owned political process” that they said should meet the legitimate aspirations of all Syrians, protect all of them and “enable them to peacefully, independently and democratically determine their own futures”.

They emphasised battling “terrorism” across the country, stressed that Syria must abide by council resolutions on non-conventional weapons, and reiterated support for UN peacekeepers and the inviolability of diplomatic premises.

Separately, a US State Department spokesman said the ceasefire in northern Syria had been extended until the end of this week.

“We continue to engage with the SDF, with Turkey about a path forward,” State Department spokesperson Matthew Miller said, adding it was not in the interest of any party to see increased conflict in Syria.

Later on Tuesday, SDF commander Mazloum Abdi said in a post on X that the group was ready to present a proposal for a “demilitarised zone” in the northern city of Kobane, with the redeployment of security forces under US supervision.

He said the proposal aims to address Turkiye’s security concerns and ensure permanent stability in the area.

There was no immediate comment from Turkiye, the SNA or the US.

Pedersen also called on the UNSC to ensure that Israel “cease all settlement activity in the occupied Syrian Golan”.

Pedersen noted Israel has conducted more than 350 strikes on Syria following the departure of the former government, including a major strike on Tartous.

“Such attacks place a battered civilian population at further risk and undermine the prospects of an orderly political transition,” he said.

The UN envoy warned against plans announced by Israel’s cabinet to expand settlements inside the Golan, occupied by Israel since 1967 and annexed in 1981.

On Tuesday, Israeli Prime Minister Benjamin Netanyahu held a security briefing inside the UN-patrolled buffer zone in the Golan Heights that Israel seized earlier this month.

“Israel must cease all settlement activities in the occupied Syrian Golan, which are illegal. Attacks on Syria’s sovereignty and territorial integrity must stop,” said Pedersen.

Pederson also called for “broad support” to end the Western-backed sanctions imposed on Syria in order to allow for reconstruction in the war-ravaged country.

“Concrete movement on an inclusive political transition will be key in ensuring Syria receives the economic support it needs,” Pedersen stated.

“The needs are immense and could only be addressed with broad support, including a smooth end to sanctions, appropriate action on designations, too, and full reconstruction.”

Western countries are wrestling with their approach to Hayat Tahrir al-Sham (HTS), which spearheaded the takeover of Damascus and is a former al-Qaeda affiliate.

Despite moderating its rhetoric in recent months, HTS has been designated as a “terrorist” group by many Western governments.

The site at al-Qutayfah, located 40km (25 miles) north of the capital, was one of several mass graves identified across the country after the collapse of the decades-long rule of the al-Assad family.

Twelve mass graves were also discovered in southern Syria. At one site, 22 bodies, including those of women and children, exhibited signs of execution and torture.

Al-Assad and his father Hafez, who preceded him as president and died in 2000, are accused of killing hundreds of thousands through extrajudicial killings, including in the country’s notorious prison system.

Ugur Umit Ungor, professor of genocide studies at the University of Amsterdam, told Al Jazeera that the discovery of the “centralised mass grave” in al-Qutayfah was “a reflection of the killing machine of the Assad regime”.

“The true scale of exactly how many mass graves are out there is only to be found in the archives of the Assad regime, that’s why it is absolutely crucial that they are handled in a professional way and that people don’t go pillaging them,” he added.

Ungor said creating a DNA depository of the families whose relatives are missing would help match the remains to a name, giving closure to those still looking for their loved ones.

The professor was among a handful of academics who received videos and other evidence from anonymous sources as part of a yearlong investigation into the burial sites.

Al Jazeera’s Mohammed Vall, reporting from Qatana, said the Syrian air force intelligence was believed to have been in charge of transferring the bodies from the hospitals – where they were collected from after having been killed in prison – and taking them to the mass graves.

“These mass graves hold the secrets of 54 years of despotism, torture and dictatorship,” Vall continued, adding, “This is only the beginning.”

Last week, Human Rights Watch visited the southern Damascus neighbourhood of Tadamon, where it found human remains that showed signs consistent with executions. The New York-based organisation called on the transitional Syrian authorities to preserve physical evidence across the country.

The commander-in-chief of the new administration, Ahmed al-Sharaa, told Al Jazeera that those who committed crimes against the Syrian people or who actively helped al-Assad commit those crimes would be brought to justice.

“We won’t give up on delivering the justice our people expect and we will not let the atrocities committed against our people be forgotten,” al-Sharaa, also known as Abu Mohammed al-Julani, said.

He added that “we’re gathering and collecting evidence” and called on the United Nations and other international institutions to help document the crimes committed by the regime.

On Monday, al-Assad put out his first statement since he was ousted, saying he fled Syria for Russia only after Damascus had fallen, and he denounced the country’s new leaders as “terrorists”.

Al-Sharaa’s Hayat Tahrir al-Sham (HTS) is listed as a “terrorist” group by many governments. It has sought to assuage fears, assuring protection for minorities, security and a peaceful political transition.