Fresh air strikes pummelled the Syrian city of Aleppo on Monday as US Secretary of State John Kerry made a desperate bid to salvage a two-month ceasefire in the war-torn country.

The top US diplomat gave some of his most downbeat comments yet after meeting the UN peace envoy on Syria, saying the conflict was "in many ways out of control and deeply disturbing to everybody in the world, I hope."

"The attack on this hospital is unconscionable," he said, accusing President Bashar al-Assad's regime of deliberately targeting three clinics and a major hospital last week. "And it has to stop."

Kerry met UN peace envoy Staffan de Mistura and the Saudi foreign minister in Geneva, but the absence of Russia cast a pall over the proceedings.

Washington and Moscow are the joint sponsors of the Syrian peace process, and de Mistura has made it clear that he sees little hope of progress without their agreement.

Kerry said he would call Russian Foreign Minister Sergei Lavrov later Monday to press for the ceasefire to be restored.

De Mistura was due to fly to Moscow for talks with Lavrov on Tuesday.

While agreeing in theory to support a ceasefire, Russia has done little to rein in Assad's forces around Aleppo, which were in action again early Monday.

More than a week of fighting in and around Syria's second city has killed hundreds of civilians, and fresh air strikes hit rebel-held eastern Aleppo in the early hours.

Several neighbourhoods, including the heavily-populated Bustan al-Qasr district, were hit, according to AFP's correspondent in the northern Syrian city.

"What is happening in Aleppo is an outrage. It's a violation of all humanitarian laws. It's a crime," said Saudi Foreign Minister Adel al-Jubeir as he met Kerry.

"It's a violation of all the understandings that were reached," he added, accusing Assad and the Russians of violating international agreements to back peace.

Despite the early-morning raids, there was a relative lull in the fighting later Monday, allowing some residents to venture out into the streets, AFP's correspondents there said, with some even opening up shops.

- 'Getting closer' -

Kerry said Washington would press moderate rebels to separate themselves from the Al-Nusra Front's jihadists in Aleppo.

Russia and Assad's regime have used the presence of Al-Nusra, which was not party to a February 27 ceasefire deal, as an excuse to press their offensive.

There is growing concern that the fighting will lead to a complete collapse of the landmark ceasefire agreed between Assad's regime and non-jihadist rebels.

Following his meeting with Kerry, the Saudi minister expressed scepticism that Assad's regime was in any way serious about the truce, and said Riyadh would continue giving weapons to the rebels.

- Aleppo toll rising -

Aleppo was initially left out of a deal to "reinforce" the February truce agreement.

The freeze in fighting, announced on Friday, applied to battlefronts in the coastal province of Latakia and Eastern Ghouta, near Damascus.

State television reported a Syrian army announcement on Monday that the freeze has been extended for another 48 hours in Eastern Ghouta, until 1:00 am Wednesday (2200 GMT Tuesday).

The same "freeze" is set to hold until 1:00 am Tuesday in Latakia, a regime stronghold.

But in divided Aleppo, the bloodshed continued unchecked.

At least 253 civilians -- including 49 children -- have been killed on both sides of the city since April 22, the Syrian Observatory for Human Rights monitor says.

The escalating violence in Aleppo has also hit medical centres, with the International Committee of the Red Cross saying four were struck on Friday alone.

Two days earlier, 30 people were killed when an air strike hit a hospital supported by Doctors Without Borders (MSF) and the Red Cross, sparking an international outcry.

The bloodshed has dampened hopes that the ceasefire could finally lay the groundwork for an end to Syria's five-year conflict.

Last month's peace talks in Geneva failed to make any headway, although de Mistura has said he hopes they can resume "during the course of May".

Syria's conflict erupted in 2011 after the brutal repression of anti-government protests and has since escalated into a complex, multi-faceted war, which has killed more than 270,000 people.

France called Monday for a ministerial meeting of the international group supporting Syria to "restore the ceasefire."

Foreign Minister Jean-Marc Ayrault said Paris was "totally mobilised" in pushing for the peace process to resume as quickly as possible.

"For that the strikes on Aleppo must stop," he said.

France calls for urgent talks to restore Syria truce
Paris (AFP) May 2, 2016 - France called Monday on the International Syria Support Group to hold urgent ministerial-level talks to restore the country's tattered ceasefire, condemning deadly air strikes by the Damascus regime.

Paris urged the 17-nation ISSG to "restore the ceasefire, reaffirm the need to protect civilian populations... and give a chance to negotiations towards a political settlement," said foreign ministry spokesman Romain Nadal.

"France forcefully condemns the (Damascus) regime's attacks that have caused many casualties (and) calls on the supporters of the regime (Russia and Iran)... to use their influence on Damascus to silence the weapons," he said in a statement.

French Foreign Minister Jean-Marc Ayrault, speaking during a trip to Mali, added that France was "totally mobilised" pressing for the peace process to resume "as quickly as possible.

"For that the strikes on Aleppo must stop," he said.

"We have told our US partners that we want the greatest pressure put on Russia to intervene with the Damascus regime" which Moscow supports, to stop the bombing of Aleppo.

The ISSG is co-chaired by the United States and Russia, which brokered the February 27 "cessation of hostilities" deal.

But the truce has been shattered in the past week, especially in Aleppo, where more than 250 civilians including some 50 children have been killed since April 22, most in air raids carried out by the Syrian regime.

US Secretary of State John Kerry, currently in Geneva in efforts to salvage the truce, said Syria's civil war was "in many ways out of control".

UN peace envoy Staffan de Mistura, who has been leading negotiations between Damascus and the opposition since the start of the year, is expected to hold talks with Russian Foreign Minister Sergei Lavrov in Moscow on Tuesday.