Russia called on Saturday for a political transition in Syria, while Switzerland said it would petition the International Criminal Court to probe war crimes in the country.
Regime warplanes carried out air strikes near the capital and a car bomb blew up in Damascus province, while gunmen shot dead an athletics champion, said the Syrian Observatory for Human Rights.
A day after UN-Arab League special envoy Lakhdar Brahimi met Russian Deputy Foreign Minister Mikhail Bogdanov and US Deputy Secretary of State William Burns, Moscow repeated its long-held position that only Syrians can decide their fate.
"In our opinion, the priority task is to immediately stop any violence and bloodshed as well as provide Syrians including internally displaced persons and refugees with humanitarian aid," the foreign ministry said.
But it added: "At the same time it is necessary to secure the launch of a political transition process in Syria aimed at enshrining in law guaranteed and equal rights of all ethnic-confessional groups of this country."
Moscow, a key Damascus ally, also reiterated its support for a transition plan that was agreed in Geneva in June but has since split world powers.
Bogdanov also met a Syrian delegation led by Michel Kilo, a prominent anti-regime activist who opposes foreign intervention, and pledged to continue "active contacts" with both Damascus and the opposition, the ministry said.
Inside Syria, regime warplanes bombarded the outskirts of Mleha just southeast of Damascus "a day after rebels assaulted an air force security building there," the Britain-based Observatory said.
The Observatory, which relies on a network of activists and medics on the ground, also reported a car bomb explosion that ripped through the Abu Arif area of Sbeineh in Damascus province causing heavy damage.
Also near Damascus, unidentified gunmen "murdered athletics champion Hisham al-Raksha, while he was in his car," said the watchdog.
At least 90 were killed in violence nationwide on Saturday, the Observatory said.
Amid unrelenting violence, Switzerland said it will file on Monday a petition signed by 52 countries calling for the ICC to open a case on war crimes in Syria, its foreign minister said.
"Serious war crimes are being committed in Syria. We must make sure they not go unpunished," Didier Burkhalter told Swiss national television TSR.
"We're submitting a proposal. Now it is up to the Security Council to decide," he added, saying the UN organ could either block or pursue the request.
Since Syria is not a party to the ICC, the world's only permanent war crimes tribunal, a UN Security Council referral is needed for the court to look into crimes committed in the 22-month conflict.
The United Nations estimates that more than 60,000 people have died since the March 2011 outbreak of the revolt, and says more than 600,000 Syrians are registered as refugees in the region.
Escalating violence has led to thousands of low and mid-level defections, when peaceful protests turned violent amid a deadly crackdown on dissent.
In a video posted on the internet on Friday, a man identifying himself as Jumaa Farraj Jassem, a senior foreign intelligence official, announced his defection. AFP was unable to verify the authenticity of the video.