By John Davison and Suleiman Al-Khalidi

BEIRUT/AMMAN (Reuters) - Rebels attacked Syrian government positions in the historic center of Aleppo on Monday in response to an offensive that cut a road leading into the opposition-held sector of the city, monitors and insurgents said.

The shelling of government-held neighborhoods and intense street fighting came days after the advance by the government side towards the Castello Road. Rebels have relied on the road for supply runs and access to Aleppo through much of Syria's civil war, and its severing effectively put opposition-held areas where some 250,000 people live under siege.

Residents contacted in the city said prices of fresh vegetables, bread and fuel had on average almost doubled in the past week with no new supplies coming into Aleppo, Syria's largest city and commercial hub before the war.

Aleppo has been a major battleground in the conflict, now in its sixth year. Fighting there escalated after U.N.-brokered peace talks and a ceasefire unraveled earlier this year.

The Syrian military said it would extend a nationwide ceasefire for another 72 hours from Tuesday, state media reported on Monday. The Syrian army and the Russian military, which backs Syrian President Bashar al-Assad, have periodically this month announced these temporary truces but continued to step up their military campaigns in major battlefields.

Aleppo's capture would be a strategic prize for Assad's government, which controls the major population centers in western Syria apart from rebel-held districts of Aleppo, and the far northern city of Idlib. Rebels hold pockets of territory elsewhere in western Syria.

Kurdish forces prevail in vast swathes along the nearby Turkish border, and Islamic State militants dominate territory in the east closer to the border with Iraq.

Early on Monday more than 300 shells fired by rebels hit western, government-held neighborhoods of Aleppo, killing five people and wounding dozens more, the Syrian Observatory for Human Rights said. State television said eight people had been killed and that the bombardments had brought down buildings.

The assault was "a response to the (government) attempts to advance", Zakaria Malahifji of the Aleppo-based Fastaqim rebel group told Reuters.

He said insurgents had already made gains, and that much of the fighting was taking place in Aleppo's ancient Old City, a renowned UNESCO World Heritage site now largely in ruins.

A witness reported fierce close-range clashes near the historic citadel where rebels killed at least 20 army troops when they blew up a tunnel they dug underneath a government post, according to the monitor.

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A Syrian state TV correspondent said there had been heavy fighting since the morning, and that the army had seen off attacking rebels, killing many.

Syrian warplanes bombarded rebel districts of Aleppo, the British-based Observatory said, with at least 10 civilians killed in a strike on Hay al Maqam. A pro-Damascus TV channel said Russian warplanes, backing the government, were bombing areas north of the city, near the Castello Road.

Jets believed to be Russian or Syrian also rocketed a fuel market in a town in the northwestern province of Idlib, killing at least 10 people and injuring scores, according to a local rescue worker near the site.

An air strike hit a local field hospital in the town of Ahsem in Idlib province, killing three people, including a child, an international charity and an aid worker said.

A statement from the Jabha Shamiya rebel group dated Sunday said the government advance near Castello Road came with the support of "allies of various nationalities, with Russian air cover and with firepower of an unprecedented intensity".

Assad is supported by Moscow, which launched air strikes in September, as well as Iranian troops and Lebanese Shi'ite Hezbollah fighters.

Hezbollah has said it sees Aleppo as the most important battle in Syria, equating it with the defense of the capital Damascus, and hundreds of its men have died in the conflict.

Assad's allies say they are battling the al Qaeda-linked Nusra Front in Aleppo. But groups fighting under the banner of the Western-backed Free Syrian Army (FSA) say they control the rebel-held part of the city.

Nusra Front said it had launched an attack in central Aleppo and made advances towards a market in a government-held area. Malahifji of the Fastaqim rebel group said there was only a small Nusra Front presence in Aleppo.

The Saudi-backed main Syrian opposition body, the High Negotiations Committee (HNC), told U.N. special envoy Staffan de Mistura in Rome that it was premature to set a date for fresh peace talks he was seeking ahead of an August deadline for the warring parties to present outlines of a political deal.

"There is a need to adopt a new strategy to push the peace process by adopting a tougher policy against the regime's violations against the Syrian people ... before calling for a new round of negotiations," the HNC statement said.

De Mistura urged no let-up in peace efforts. "More than ever, the key is a possible deal between Russia and America, because they are the ones who ... pulled off the miracle of the two-month truce," he said, referring to the "cessation of hostilities" deal that calmed much of Syria before collapsing.

(Additional reporting by Tom Perry and Crispian Balmer in Rome; Editing by Mark Heinrich and Jonathan Oatis)