Russia's Foreign Ministry partially blamed the United States on Tuesday for a recent mortar attack on the Russian embassy in the Syrian capital Damascus.

"We are considering the shelling of the Russian embassy in Damascus to be a consequence of actions by those such as the United States and some of its allies who are instigating a continuation of the bloody conflict in Syria by catering to militants and extremists of various sorts," the Russian Foreign Ministry said in a statement.

The attack occurred on Monday, the day that the US announced it was suspending its cooperation with Russia on Syria amid Russia's continued bombing of one of Syria's most populous cities, Aleppo.

The northern city of Aleppo is divided between a government-held western sector and the rebel-held east, where an estimated 250,000 to 300,000 civilians are under siege by government forces backed by Russian airstrikes.

Russia denounced the embassy attack as a "crime committed by terrorists" and said it was most likely perpetrated by the al-Qaeda-linked Fatah al-Sham Front, formerly known as al-Nusra Front, or Islamist group Faylaq al-Rahman.

One of the mortar shells exploded near the embassy's residential complex, and "by sheer luck, none of the embassy's employees was hurt," the Foreign Ministry said.

Russia's Defence Ministry also announced Tuesday that it had sent an S-300 anti-aircraft missile system to Syria, specifically to protect Russia's naval facility in the coastal Syrian city of Tartus.

The US on Tuesday questioned the purpose of the Russian anti-aircraft deployment.

"Last I checked, the Russians said that their primary goal was to fight extremism, [Islamic State and al-Nusra Front], in Syria. And neither one has an air force," Pentagon spokesman Peter Cook said.

"So I would question just what the purpose of the system is ... Maybe the Russians have a better explanation."

Syrian state media reported that several people were killed and dozens injured in a rebel attack on government-held parts of western Aleppo.

Russia has supported the Syrian government with a bombing campaign against rebel groups in the country for more than a year. The US and some Middle Eastern powers have backed certain rebel groups seeking to overthrow the Syrian government.

However, both the US and Russia agree on the need to eliminate UN-designated terrorist groups that have gained significant territory in the war-town country in recent years.

US Secretary of State John Kerry said Tuesday that despite suspending coordination with Russia, the US is "not giving up" on the Syrian people.

"We are going to continue to try to find a way forward in order to end this war," Kerry said at a think-tank event in Brussels. He noted that the US would do "everything possible" to find a way forward with the international Syria support group, the United Nations or in smaller multilateral meetings.

The Syrian Observatory for Human Rights, a Britain-based monitoring organization, said more than 400 cilivians have been killed in Aleppo since a US- and Russian-backed ceasefire collapsed about two weeks ago.

In a Kurdish-held part of north-eastern Syria, a suicide attack on a wedding on Monday night killed more than 30 people, with a leader of the opposition Kurdish Yekiti party reported among the dead.

UN human rights chief Zeid Ra'ad Al Hussein said Tuesday in Geneva that limiting the veto power of UN Security Council member states such as Russia would enable Syria war crime cases to be brought to the International Criminal Court in The Hague.

The current attacks against civilians, medical units and aid workers may amount to war crimes or even worse, said Zeid, a Jordanian prince.

Vitaly Churkin, Russian ambassador to the UN, rejected Zeid's call noting it wasn't "his responsibility to discuss veto powers."

"Unfortunately, my good friend has been overstepping the limits of his responsibilities quite a bit and this is unfortunate," Churkin said.

Meanwhile, UN Secretary General Ban Ki-moon said in Strasbourg that he will strongly urge the United States and Russia to resume their negotiations over Syria, at talks this week with US Secretary of State John Kerry and high-level officials from Moscow.

Speaking to reporters, Ban described the situation in Aleppo as "really heart-breaking and most troubling."

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