Syria's opposition leaders have turned their back on international talks, saying the world's failure to stop the violence is "shameful".
After missiles killed dozens in Aleppo on Friday, the SNC released a statement saying the move was to protest the lack of international condemnation of the "crimes committed against the Syrian people".
"Hundreds of civilians have been killed by Scud missile strikes. Aleppo, the city and the civilization, is being destroyed systematically," the statement said.
"The Russian leadership especially bears moral and political responsibility for supplying the regime with weapons," it said, referring to Russia's status as a leading ally of Syrian President Bashar al-Assad.
"In protest of this shameful international stand, the coalition has decided to suspend its participation in the Rome conference for the Friends of Syria and decline the invitations to visit Russia and the United States."
The Friends of Syria is a collection of dozens of countries trying to find a solution to the Syrian crisis.
Speaking to Al Jazeera from Cairo on Saturday, Louay Safi, chair of the SNC's political office, said the group wants the UN Security to Council to "make a clear condemnation of [Damascus] using these weapons against populated areas".
Al Jazeera's Nisreen El-Shamayleh, reporting from Antakya in Turkey, said that the SNC felt promises of help from international community has been very slow and that international community was not keeping the promises it made three months ago.
"It is not really turning its back on the international community. It is still calling on the international community to help it with negotiations it wants to start with the Syrian government, she said.
Aleppo attack
At least 29 people were killed and dozens more wounded after rockets hit two eastern districts of Aleppo, according to anti-government activists.
Friday's assault - involving three surface-to-surface missile strikes - caused several buildings to collapse, according to the Syrian Observatory for Human Rights (SOHR), a UK-based anti-government rights group.
There were children among the dead, the SOHR said.
In a video posted to YouTube, a massive cloud of dense smoke was seen rising from the neighborhood at dusk after one of the missiles struck.
Other video showed burning buildings, and people carrying the wounded to ambulances and cars.
Earlier on Friday, the SNC said in Cairo that it was pushing forward with efforts to name a transitional government in the coming days.
Walid al-Bunni, an SNC spokesperson, said that the transitional set-up would control rebel-controlled areas in Syria.
He said that the prime minister would be named on March 2 during a meeting in Istanbul, Turkey, after consultations were held within the opposition.
Bunni said that the SNC was open to a negotiated end to the conflict, but that it would not negotiate with Assad.
Assad and government officials involved in the killing of rebels must step down and face charges, he said.
PHOTO CAPTION
Forces loyal to Syria's President Bashar al-Assad deployed from al-Sabaa Bahrat district move on their armored vehicles towards the old souk of Aleppo February 21, 2013.
Aljazeera