BEIRUT – Russia said Sunday it has no intention of pushing for the ouster of President Bashar Assad, as international negotiators seeking a way out of the escalating Syrian crisis again failed to reach a breakthrough.

Meanwhile, the Syria turmoil continued to spill over its borders, as four more people were killed in the latest spasm of Syria-related violence in the tense northern Lebanese city of Tripoli.

And inside Syria, another day of fierce clashes and government bombardment was reported in the suburbs of Damascus as government troops battled rebels intent on cutting off the capital and its international airport.

Violence in Syria has long been outpacing efforts to reach a diplomatic solution. International mediators have stepped up efforts to broker a peace in recent days as clashes have intensified and fears have risen about the government’s potential use of chemical weapons on its own citizens.

The sense that Assad’s rule is weakening amid rebel gains has prompted speculation that Moscow was finally willing to tell its longtime ally that it was time for him to go. U.S. and Russian talks in Dublin last week with the U.N.’s Syrian envoy, Lakhdar Brahimi, added fuel to speculation that Russia — which has on three occasions blocked proposed United Nations actions against Assad — was ready to cut its ally loose.

But Russian Foreign Minster Sergei Lavrov made it clear Sunday that Moscow had not soured on the Syrian leader.

“We are not conducting any negotiations on the fate of Assad,” Lavrov told reporters in Moscow. “All attempts to portray things differently are unscrupulous, even for diplomats of those countries which are known to try to distort the facts in their favor.”

The latter comment seemed aimed at Western officials who had hinted that Moscow was ready to help expedite Assad’s departure after almost 21 months of civil conflict, tens of thousands of deaths and vast infrastructure damage.