Chechen rebels held onto the presidential palace in Grozny today, turning back a furious and bloody Russian assault that has seen heavy casualties on both sides. Despite being outnumbered and poorly armed, the rebels pushed the Russian troops out of Grozny's center, forcing Russian President Boris Yeltsin to send reinforcements. Civilian casualties continued as Russian jets, trying to destroy a bridge about seven miles from Grozny, killed at least 10 people in their cars. But Russian soldiers have suffered as well: the military acknowledged that Chechen rebels have captured or destroyed several dozen armed personnel carriers. The rebel soldiers in the secession-bound republic are packed inside the presidential palace, 1,000 miles south of Moscow. Just outside is a scene of carnage: strewn bodies and burning military vehicles.Meanwhile, opposition to the Chechnya assault is building in Moscow, says TIME correspondent Ann Simmons. "Many Russian parliamentarians are saying this is the beginning of authoritarianism by Yeltsin," says Simmons. Still, don't expect Yeltsin to buckle. "The Chechens are not going to concede -- that much is clear. Given that, Yeltsin is obliged to see this through," Simmons says.