Grozny, the capital, came under heavy artillery bombardment overnight, but some roads to the city still remained open. A Chechen spokesman said the assault was the most intense "since the beginning of the second Chechen war", which started three months ago. The first war, which left the republic with de facto independence, lasted from 1994 to 1996.
General Valery Manilov, the Russian first deputy chief of staff, said: "The aim of the third phase of the anti-terrorist operation is to complete the destruction of bandit groups and their bases in the foothills and mountainous areas of the Chechen republic."
The Russian troops will have to advance along poor roads through steep forested valleys where they suffered heavy casualties in the last war.
Russia still hopes the Chechens will give up Grozny without a fight. President Boris Yeltsin has offered an amnesty to rebels who have not committed "serious crimes".
The Chechen high command is concerned it has lost Gudermes, the republic's second city, and Achkhoy-Martan without a fight. A senior Chechen commander said those responsible for their surrender would be held to account under "war-time laws."
Yesterday the Chechens said Ramdan Tsakayev, one of their most experienced commanders, had been killed. "Tsakayev's truck blew up when the shells he was transporting to the front line exploded."