UN chief Ban Ki-moon warned world powers they must overcome their rivalries to put an end to the "proxy war" in Syria, as deadly fighting raged in Damascus and the country's second city Aleppo.

Ban spoke on Friday ahead of a UN General Assembly vote that overwhelmingly condemned the Security Council for its failure to act and slammed President Bashar al-Assad's use of "heavy weapons" in the nearly 17-month civil war.

Shells rained down on rebel positions in Aleppo as fighting was reported in Syria's commercial capital and in Damascus, with the Syrian Observatory for Human Rights reporting at least 70 people killed across the country.

At the same time, new weekly anti-regime protests were held across Syria in solidarity with the eastern province of Deir Ezzor, which troops have pounded for weeks.

The day's slogan was "Deir Ezzor -- victory comes from the east", and the Observatory reported claims that 70 percent of the strategic oil-producing province that borders Iraq was now in rebel hands.

In Aleppo, hundreds gathered in Al-Shaar neighbourhood chanting: "The people want the execution of Bashar!" and "The people want freedom and peace," a reporter at the scene said.

As jet fighters and helicopter gunships swooped over the city, the Observatory reported demonstrations in several neighbourhoods and fierce clashes in the rebel-held Salaheddin district.

A Syrian security source said troops were "testing the terrorists' defence systems... before annihilating them by carrying out a surgical operation".

In Moscow, the Russian foreign ministry expressed serious concern over rebel attempts to gain control of Aleppo and condemned foreign nations for providing the opposition with military supplies.

"Moscow is very worried by the dangerous development in the situation, the violence and provocations aimed at expanding the scope and the cruelty in the civil war," the ministry said.

The Observatory also reported protests in the Kurdish region of Hasakeh, Daraa province in the south and in the northwestern province of Idlib, where one demonstrator was shot dead.

Also in Idlib, five rebels were killed in an army ambush, the Observatory said, while the official SANA news agency said regime forces killed 17 "terrorists" in Aleppo.

In Damascus, six civilians were killed as loyalist forces moved on rebels a day after shelling killed 21 civilians at the Palestinian refugee camp of Yarmouk, the Observatory said.

At the General Assembly, Ban evoked the UN's failure in the 1995 Srebrenica massacre in Bosnia and warned the divided Security Council that "the immediate interests of the Syrian people must be paramount over any larger rivalries of influence".

The secretary general said growing radicalisation and extremism had been predicted at the start of the conflict in March 2011.

"The next step was also forewarned: a proxy war, with regional and international players arming one side or the other. All of these dire predictions have come to pass," Ban told the General Assembly.

He turned his fire on the Security Council, which he said had become "paralysed" by divisions over Syria. "Now, with the situation having worsened, they must again find common ground," Ban said.

After his address, the General Assembly overwhelmingly passed a Saudi-drafted resolution criticising the Security Council's failure to act and condemning Assad's use of heavy weapons.

The resolution said members deplored "the Security Council failure to agree on measures" to make the Syrian government carry out UN demands to end almost 18 months of fighting.

The resolution, which condemned President Bashar al-Assad's use of "heavy weapons including indiscriminate shelling from tanks and helicopters", was passed by 133 votes with 12 countries against and 31 abstaining.

"Despite the continued opposition of an increasingly isolated minority, the overwhelming majority of UN members clearly stands resolutely with the Syrian people," commented US ambassador Susan Rice after the vote.

The French and British governments also welcomed the resolution. The vote shows that "the international community condemns the massive and systematic violations of human rights in Syria and the use of arms of war by the regime against its people", said France's Foreign Minister Laurent Fabius.

But Russia's UN ambassador Vitaly Churkin warned it gave "blatant" support to Syrian rebels and that its backers were the countries providing "mercenaries and arms" to the opposition.

China's deputy UN ambassador Wang Min said pressuring only the Syrian government will "cause further escalation of the turmoil and let the crisis spill over to other countries in the region".

Russia and China have so far vetoed three Security Council resolutions on Syria.

Syria strongly opposed the resolution and its UN envoy, Bashar Jafaari, accused Saudi Arabia, Qatar and other Gulf states of arming rebel groups.

The ambassador said he and his family had been the target of death threats.

"There have been several threats of murder against me and various Syrian diplomats from sites that exist in Saudi Arabia and Qatar and the United States," he told the General Assembly.

While US envoy Susan Rice welcomed the vote, many countries expressed reservations. South Africa, which voted in favour, said the resolution should have been tougher on the Syrian opposition.

The head of the opposition Syrian National Council said the resolution showed that the Assad regime had lost legitimacy.

"This vote confirms that... the international community does not believe in its legitimacy anymore," Abdel Basset Sayda told a news conference in Iraqi Kurdistan.

He also said Syrian rebels would not pull out of Aleppo. "The Free (Syrian) Army did not withdraw, and will not withdraw from Aleppo, and we are in contact with them to provide them with supplies," Sayda said.

Though the resolution is not legally binding, there was increased attention on the General Assembly action after the resignation on Thursday of UN-Arab League envoy Kofi Annan and the mounting battle for Aleppo.

Annan complained that a peace plan he negotiated never received the backing it deserved and voiced regret at the "increasing militarisation" of the conflict.