The announcement came after the coalition had said it would form a government to run "liberated areas" of Syria, and as international condemnation mounted against Thursday's devastating attacks in Damascus that left around 100 people dead.
In further violence Friday, monitors said more than 12 people had been killed when buildings collapsed after a missile strike on the city of Aleppo.
The National Coalition said it was pulling out of meetings in Italy, Russia and the United States, to protest against the "shameful" lack of international condemnation of "crimes committed against the Syrian people".
The group had been due to attend a Friends of Syria meeting in Rome next Thursday where US Secretary of State John Kerry is also expected. National Coalition chief Ahmed Moaz al-Khatib had also been invited to Moscow.
"The international silence on the crimes committed every day against our people amounts to participating in two years of killings," said the statement.
"We hold the Russian leaders in particular ethically and politically responsible because they continue to support the (Damascus) regime with weapons," the National Coalition added.
Already Friday, coalition spokesman Walid al-Bunni had announced plans for a government for "liberated areas" following a meeting in Cairo.
They would decide on its composition and choose its leader at a meeting on March 2, he added.
Coalition members said the meeting would be held in Istanbul, while Bunni said it was hoped the government would be based in rebel-held territory inside northern Syria.
The opposition umbrella group had been discussing a proposal by chairman Ahmed Moaz al-Khatib to hold direct talks with President Bashar al-Assad's regime.
The group has refused to meet Assad himself, or the security or military command. Khatib himself has made it clear the offer was only to those without "blood on their hands".
The Arab League and the United States, vocal critics of the Assad regime, have welcomed the initiative, as have Iran and Russia, both close to the Damascus regime.
Earlier, international peace envoy Lakhdar Brahimi said Thursday's attacks in Damascus had left about 100 people dead -- substantially more than a previous toll of 60 people -- and wounded another 250.
Describing the attack as a "war crime", the UN-Arab League envoy added in a statement: "Nothing could justify such horrible actions that amount to war crimes under international law."
European Union foreign policy chief Catherine Ashton also condemned the Damascus attack
"Nothing can justify an act of such brutality that killed so many people, mostly civilians including children," Ashton said in a statement Friday.
Both the regime and its opponents have blamed the attack near the entrance of the ruling Baath party's main offices on "terrorists".
Another 22 people were killed in an apparently coordinated triple bombing targeting security headquarters in the northern Damascus district of Barzeh the same day, including 19 members of the forces, said the Syrian Observatory for Human Rights.
On the violence in the northern city of Aleppo, Observatory director Rami Abdel Rahman said at least 14 people were killed and dozens wounded after three missiles hit the Tariq al-Bab district.
The Britain-based Observatory said the number of victims was likely to rise as many people were trapped under the rubble.
Elsewhere, eight civilians were killed in air strikes on Harasta just northeast of Damascus; and another 10 people were killed by shelling that targeted the Grand Mosque of Harak, in the southern province of Daraa, the Observatory said.
The watchdog, which collects reports from a wide network of activists and medics on the ground, gave an initial toll of 99 people killed nationwide on Friday.
Despite the increasing brutality of the conflict, which has left an estimated 70,000 people killed, demonstrations continue to be held every Friday nationwide.
The Observatory said one person was killed and many critically wounded after security forces opened fire on demonstrators in the northern city of Raqa.