(CNN) Fierce fighting in the embattled Syrian city of Aleppo has claimed the lives of more civilians -- including children -- on both sides of the front lines in the past 48 hours.

Four children were among eight people killed Wednesday in rebel shelling on government-held parts of western Aleppo, according to the Syrian Observatory for Human Rights , a UK-based monitoring group.

The deaths came a day after five children were killed when rebels shelled a nursery in another government-held neighborhood of the city.

Meanwhile, regime warplanes conducted at least 20 airstrikes on the rebel-held neighborhoods in eastern Aleppo overnight into Thursday, the observatory reported, saying the exact number of dead and wounded is unclear.

However, the White Helmets -- a volunteer civil defense group -- said at least 13 people were killed and more than 25 injured after airstrikes targeted neighborhoods in the east of the city.

The group said it expected this number to rise.

Russia's Ministry of Foreign Affairs said the area around its embassy in the Syrian capital, Damascus, came under mortar attack Wednesday, adding that the shells appeared to be from a rebel-held area.

One mine landed on the roof of a nearby school but did not explode, it said. "The premises of the Embassy campus were littered with fragments following the attack. None of the Embassy staff were injured."

Fresh Syria talks

Meanwhile, US Secretary of State John Kerry will meet Saturday with foreign ministers from Russia and regional powers with influence over the war in Syria.

They will "discuss a multilateral approach to resolving the crisis in Syria, including a sustained cessation of violence and the resumption of humanitarian aid deliveries," the State Department said Wednesday.

The Russian Foreign Ministry confirmed the meeting in Lausanne, Switzerland.

Staffan de Mistura, UN special envoy for Syria, will also attend, his deputy, Ramzy Ezzeldin Ramzy, told reporters Thursday in Geneva, Switzerland, without elaborating on what might be on the agenda.

The talks in Lausanne come at a time when Moscow faces mounting pressure over the deaths of civilians in the Syrian military's Russian-backed assault on Aleppo.

UN: Situation in Aleppo is 'dire'

Ramzy said the people in the besieged city had seen "no relief" in the past week.

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"Both sides of the city are subjected to extremely difficult circumstances but certainly much more on the eastern side," he added.

The health situation in eastern Aleppo is "dire," he said, and the capacity to treat emergency cases is minimal after repeated strikes on hospitals.

Hundreds of people are awaiting medical evacuation from eastern Aleppo, Ramzy said, but cannot do so without a ceasefire. "More than 200 are in critical situation, but I also heard the figure of 400 children that need to be evacuated," he said.

The only positive development is that the supply of running water to eastern Aleppo has been partially restored, he said, after the repair of a pumping station put out of action by bombing.

Ramzy said de Mistura's appeal to fighters from the former al Nusra Front to leave Aleppo -- a proposal that won Russia's backing -- had received a "negative response" from the group now known as Jabhat Fateh al-Sham.

"Our understanding is that this particular appeal has found resonance in certain quarters, and they are working to make it happen, and we hope that this will be the case," he said. "There are parties on the ground who have influence, and they are the ones who can make it happen. We will see."

France wants dialogue with Russia

France is also taking diplomatic steps after days of tension with Russia over Syria.

French Foreign Minister Jean-Marc Ayrault spoke with his Russian counterpart, Sergey Lavrov, by phone Thursday, the French Foreign Ministry said.

France and Russia FMs spoke by telephone this morning. @JeanMarcAyrault reaffirmed France's will to continue dialogue with Russia. — France Diplomacy (@francediplo_EN) October 13, 2016

The two ministers discussed the situation in Syria, the ministry said, with Ayrault underlining the urgent need to break the current impasse and halt the bombardment of Aleppo to allow in humanitarian aid and open the possibility of renewed negotiations toward a political solution in the Syrian conflict.

The Kremlin said Tuesday that Russian President Vladimir Putin had canceled a planned visit to France next week. The move was an apparent snub to French President François Hollande, who suggested Moscow was guilty of war crimes in Syria.

On Saturday, Russia vetoed a UN Security Council resolution aimed at ending Syrian regime airstrikes on Aleppo and allowing humanitarian aid into the city. France and Spain had put forward the resolution.

Lavrov blames US for ceasefire collapse

Lavrov, the Russian foreign minister, told CNN he hoped that the weekend discussion in Switzerland might "launch a serious dialogue on the basis of the principles contained in the Russian-American deal," the ceasefire agreement that collapsed last month.

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He pointed the finger at the United States for the failure of the deal.

"The violation of the ceasefire happened by the American coalition who attacked the Syrian government, which they were not supposed to do, and which they said they would never plan," Lavrov said.

The days-long deal crumbled after a strike by US-led coalition warplanes on a Syrian army post killed dozens of troops. The US military did not dispute the strike but characterized it as "unintentional" and relayed its "regret" to Syria through Russia, saying the intended target had been ISIS.