They said the Russians had pounded the capital of the breakaway republic with bombs and missiles at regular intervals the previous night, forcing residents into makeshift basement shelters.
"I was lying in bed and I was tossed right out," said Lidia Bekova, 43, as she stood in a dismal rain Monday afternoon in the center of this village just outside the Chechen border, about 35 miles from Grozny.
"It's just impossible to stay," said a fellow refugee, Umar Makhuarov, 40. "They're bombing all the time now. The children are frightened."
At the same time, Chechen defenders were mounting fierce resistance on the approaches to the capital, and Russian troops were engaged in some of their heaviest fighting yet.
The fighting around Grozny prompted the head of Chechnya's armed forces to appeal to the rest of the Caucasus to come to the Chechens' aid.
"I call on the people of the entire Caucasus region to rise up and repel the aggressor," Colonel Aslan Maskhadov said in a television address, raising the specter of the conflict spreading along Russia's volatile southern rim. He spoke before Russian bombs knocked out the capital's television transmission tower.
Refugees here confirmed that Russian air strikes on the television tower and main power station had knocked all channels off the air and left many parts of the city without power.
They said the fighting had disrupted food supply to the city, leaving most store shelves barren and creating long lines at those that were not.
"We don't even have bread," said Asya Ozdoyeva, 38, a sales clerk. "Everything has been bought up. You can't even find a pack of chewing gum They just want to kill the people with hunger and cold."
Ozdoyeva said she fled Grozny on foot Monday with her three sons, ages three, seven and 16. She said she walked for nearly two hours, carrying her youngest son most of the way, until a driver took pity on her and asked two male passengers to get out to make room for her and her family.
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