The attacks around a lightning offensive by Islamist insurgents, who have seized Syria's second city Aleppo, were deepening the suffering endured by millions in the country after years of civil war, the United Nations rights office said.

"UN High Commissioner for Human Rights Volker Turk is extremely concerned about the escalation in hostilities," his spokesman Jeremy Laurence told reporters in Geneva.

"This is tragic, as many have lived in misery since the outbreak of conflict nearly 14 years ago," he said.

Fighting in Syria has involved foreign powers and jihadists leaving an estimated 500,000 people dead.

The conflict had been mostly dormant, with Assad back in control of much of the country until last week, when a militant alliance led by the Islamist Hayat Tahrir al-Sham (HTS) began its offensive.

The fighting has killed more than 457 people, including at least 72 civilians, according to the Syrian Observatory for Human Rights.

Nearly 50,000 people have fled their homes in recent days, the UN said Monday.

Laurence said the rights office had documented "a number of extremely concerning incidents resulting in multiple civilian casualties, including a high number of women and children."

"The hostilities are resulting in destruction and damage to civilian objects, including health facilities, buildings hosting institutions dedicated to education, and food markets," he said.

In parallel, he warned that "life-saving assistance is largely unable to reach the conflict zone".

"Hospitals and public health facilities in Aleppo are running at maximum capacity and have limited staffing and supplies."

The UN's World Health Organization said the fragile healthcare system was "under immense strain".

"Referral hospitals are overwhelmed with trauma cases, with thousands of injuries admitted in the last four days alone and doctors and nurses working around the clock to save lives, even at great personal risk to themselves and their families," WHO's acting representative in Syria Christina Bethke told reporters by video from Damascus.

She said that prior to the escalation, there had been 42 functioning or partially functioning hospitals in Aleppo.

"Today, fewer than eight hospitals continue to operate at minimal capacity," she said.