Heavy fighting claimed lives in the besieged Chechen capital of Grozny and surrounding areas on Sunday, as the Russian military pressed ahead in efforts to move deeper into the region. Russia's acting President Vladimir Putin told Russia's ORT television on Saturday night that, despite setbacks, he was confident government troops would overcome resistance and capture the city. But it seems there's little left to fight for - most of the remaining residents huddle in basements in what is left of the ruined city. Chechnya's capital city, Grozny, shows the mark of months of fighting. Residents huddle in basements, as rebels walk warily through the streets. On Sunday, there were reports of heavy fighting between Russian troops and the rebels, as Russia renewed its efforts to capture the city. An oil depot at the city's main refinery caught fire, after bombing by Russian warplanes. Though battered and bruised, Chechen rebels insist they're still in control. SOUNDBITE: (Russian) "The situation in Grozny is normal, the Chechens control all of the city... Our mood and battle spirit are high as ever...We sustained no losses - the Russian forces did." SUPER CAPTION: Kizir Khachukaev, Rebel Commander But his confidence doesn't stop a last minute prayer. For months, Russia's military has pounded the city of Grozny with bombs and shells. It's sent in small groups of soldiers to try to gain ground. Grozny residents say no matter how much the fighting escalates, they'll stay. SOUNDBITE: (Russian) " Here is my home and I won't leave no matter what. This is my home - whether I'll be dead or alive." SUPER CAPTION: Malika, Grozny resident But it's likely that resolve will be tested. On Russian television on Saturday night, acting President Vladimir Putin said despite setbacks, government troops would overcome Chechen resistance and capture Grozny. He has vowed there'll be no repeat of the 1994-1996 Chechnya war, when rebel attacks in Grozny's streets, devastated Russian troops. You can license this story through AP Archive: http://www.aparchive.com/metadata/youtube/f5ccd4e771f9c687575a99d1562dd40e Find out more about AP Archive: http://www.aparchive.com/HowWeWork