BEIRUT — A top Syrian minister on Tuesday held out the prospect of strongman Bashar Al-Assad stepping down as part of a negotiated settlement as deadly clashes broke out between supporters of Syrian regime and the opposition in neighboring Lebanon. In Syria itself, at least 58 people were killed nationwide, among them women and children, activists said, reporting relentless shelling and fighting across swathes of the main battleground of Aleppo as well as around the capital. The comments from Syria's Deputy Prime Minister Qadri Jamil came following talks with Foreign Minister Sergei Lavrov and other Moscow officials who are keen to keep their sway over the Soviet-era ally in case of the fall of Assad. Jamil rejected the idea of making Assad's resignation the condition for any future negotiations — a demand made not only by the armed opposition but also Washington and several big European states. But he said the president's departure could be a topic of discussion. “As far as his resignation goes — making the resignation itself a condition for holding dialogue means that you will never be able to reach this dialogue,” said Jamil in remarks translated into Russian. Russia on Tuesday warned the West against any unilateral action on Syria. Lavrov met China's top diplomat and a Syrian government delegation in what appeared to be a push to keep diplomacy going at a time when fewer Western and Arab governments believe that a UN-backed peace plan can end the violence. US pressure on Syria escalated further on Monday when President Barack Obama implicitly threatened to launch an attack should the Damascus regime deploy a chemical weapons stockpile it acknowledged having only last month. The US leader said pointedly that he had not ordered military engagement against the Syrian regime “at this point”. But Assad's use of chemical weapons “would change my calculations significantly,” said Obama. Lavrov said at the meeting with Dai that Russia and China base their diplomatic cooperation on “the need to strictly adhere to the norms of international law and the principles contained in the UN Charter and not to allow their violation”. In one of the latest battle zones, Syrian troops and tanks overran the Damascus suburbs of Mouadamiya on Tuesday, killing at least 20 young men and burning shops and houses before pulling back, residents and opposition activists said. The bodies of the men, mostly shot at point-blank range, were found in basements and looted premises, bringing to 50 the death toll from the army's two-day-old offensive to drive rebels from the Sunni Muslim suburb in the southwest of the capital. “People are just starting to get out of their homes to see the destruction,” said one activist who gave her name as Hayat. Opposition sources said Free Syrian Army rebels left Mouadamiya at dawn under heavy aerial and ground bombardment. The sectarian faultline also flared in neighboring Lebanon, where four people were killed and more than 60 wounded in the northern port city of Tripoli, security and medical sources said on Tuesday. Gunmen in the Sunni district of Bab Al-Tabbaneh and their Alawite rivals in Jebel Mohsen exchanged gun and grenade fire in sporadic fighting overnight and into the day, despite action by Lebanese troops deployed in the port city, residents said. Turkey is investigating possible Syrian links to Monday's deadly car bomb attack near its southeastern border, officials said on Tuesday, underscoring fears that the conflict in Syria is fuelling instability on its own territory. A car packed with explosives blew up close to a police station in the industrial city of Gaziantep, around 50 km from the Syrian border, late on Monday, killing nine people including a 12-year-old child. — Agencies