Photograph: EPA/STRINGER

Humanitarian routes to evacuate sick and wounded Syrians from besieged eastern Aleppo should be established, the World Health Organization (WHO) urged Tuesday, as rescue workers reported 13 more civilians killed in airstrikes on the rebel-held area.

More than 200 people were taken to hospitals in the city's east last weekend, but there remain only some 35 doctors to treat them, the WHO said in a statement.

Airstrikes by the Syrian government and Russia have killed 262 people in eastern Aleppo, including 42 children, since September 19, when a ceasefire brokered by the US and Russia collapsed, according to the Britain-based Syrian Observatory for Human Rights.

Last week, the government announced the start of a ground offensive in Aleppo, Syria's largest city before the war and now a battleground divided between a government-held western sector and the rebel-held east.

"All access routes to east Aleppo are closed, leaving no options for the civilian population to leave the besieged area," the statement said.

"The remaining 25 health facilities in east Aleppo city are on the verge of complete destruction, including seven hospitals that are fully or only partly functioning," the statement added.

An estimated 300,000 people in the east have been under siege since July, with residents reporting declining supplies of basic goods, including food and medicine. Water supplies have also been badly damaged.

The United States on Tuesday announced 364 million dollars in additional humanitarian aid for Syrians both within the country and in neighbouring countries hosting refugees.

In announcing the aid, US Assistant Secretary of State Anne Richard called the regime's continued denial of safe passage for aid convoys "unacceptable" and reiterated the call "for sustained and unimpeded humanitarian access to Aleppo and to all those in need throughout Syria and around the region."

The pledge brings the total amount of US humanitarian assistance in response to the conflict to 5.9 billion dollars.

On the ground, heavy clashes erupted Tuesday between opposition rebels and Syrian regime troops in Aleppo's Old City, the Observatory said.

A source close to the Syrian government, speaking anonymously as he was not authorized to brief the media, said its forces had begun their ground assault on the east from four directions.

State news agency SANA later said that government forces had captured the Old City's al-Farafira district.

Observatory director Rami Abdel-Rahman confirmed that regime forces had taken "two or three buildings" in the Old City but said there was no major offensive and characterized clashes in other parts of Aleppo as "to-and-fro" fighting.

A local rebel commander denied that the regime forces had gained ground but said they were massing troops on all fronts in the city.

There were also heavy airstrikes in the area, Abu Ahmed, a field commander in the Nureddine Zenki rebel group said.

Fresh airstrikes in eastern Aleppo killed 13 people, Ibrahim al-Hajj of the White Helmets rescue organization told dpa.

The raids appear aimed at weakening the rebels' positions and allowing the pro-government forces to eventually stage a full-on ground assault on the eastern areas.

The US, which earlier this month agreed an abortive Syria ceasefire deal with key government backer Russia, on Monday accused Moscow of a "concerted campaign... to bomb civilians into submission."

In Berlin, Chancellor Angela Merkel called the recent violence against the civilian population in Aleppo "absolutely unacceptable" and a "major setback."

She called for renewed efforts to reintroduce a ceasefire, adding that it was up to both Russia and the Syrian President Bashar al-Assad to help end the fighting.

The Observatory meanwhile said that 12 people, including five children, had been killed by Turkish border guards over the previous 24 hours while trying to cross into Turkey.

All the incidents took place on the border with Kurdish-controlled areas of Syria, the monitoring group said.

Turkey describes the dominant Syrian Kurdish forces - the main US ally on the ground in Syria against Islamic State extremists - as terrorists due to their links with banned Kurdish rebels operating inside Turkey.

The Observatory, which tracks violence across Syria, said it had documented the shooting dead of nearly 145 people, among them 29 children, by Turkish border guards while trying cross from Syria since the start of the year.

Turkey, a main backer of Syrian opposition forces fighting to topple al-Assad, has mostly closed its borders to Syrian refugees for over a year, apart from exceptional humanitarian cases.

Turkey hosts some 2.7 million registered Syrian refugees, over half the total of 4.8 million that the UN says are currently in neighbouring and North African countries.

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