Fierce street battles have erupted in the Chechen capital, Grozny, where Russian troops backed by helicopter gun ships have renewed their efforts to break through to the centre of the city.
Clashes in towns and villages east of Grozny, which were seized by Chechen fighters in surprise raids during a weekend lull in the fighting, are also reported.
Russian military commanders say federal forces now have full control over the key towns of Argun, Shali and Gudermes.
But they have also admitted that rebel fighters were still holding parts of Shali and Argun, according to Russian news reports.
Back on the attack
The Russians' return to the offensive in Grozny follows a self-imposed, three-day truce over the weekend which coincided with the Orthodox Christmas and the end of the Muslim holy month of Ramadan.
According to reports from Russia, Mi-24 attack helicopters supported troops as they inched towards the centre of the capital.
The reports say federal troops also beat back an overnight attempt by about 30 trapped Chechen fighters to break out of a Grozny suburb.
Russian troops say they have also seized a strategic height in the Sharoi district in Chechnya's southern mountains which allowed them to cut reinforcements and supplies to the rebels, Interfax news agency reported.
Worst set-back
The devastating rebel counter-attacks at the weekend - Russia's worst setback since the campaign began almost four months ago - inflicted heavy losses and humiliation on Russia's military command.
On Tuesday, acting President Vladimir Putin approved a new strategy to combat the rebels, including tighter security and a broader role for civilian law enforcement agencies in Chechnya.
Click here for a map of the region
The new policy means that all Chechen youths aged 10 and over are to be automatically treated as rebels and detained for "thorough" checks.
Declaring that new "tougher tactics" were essential, Russia's senior commander Viktor Kazantsev acknowledged "mistakes" had been made when federal troops first took the areas which had been retaken by the Chechens.
Call for dialogue
On Wednesday, Chechen leader Aslan Maskhadov reiterated calls for a political dialogue with Russia before the situation in the rebel region finally went out of
control, Interfax news agency said.
But in Russia, Defence Minister Marshal Igor Sergeyev was quoted by Russian news agency Itar-Tass as saying Russian forces would see the campaign through to its logical conclusion, and cast doubt on the idea of talks with Chechen officials.
Human rights group Amnesty International urged Russian troops and Chechen fighters to allow residents of Grozny to flee the city in safety.
"People who remain in Grozny are running out of food and supplies," the London-based group said in a statement.
It is unclear how many civilians are trapped in the capital. Russian authorities have said about 20,000 people are still in the devastated city, but Chechen fighters say the number is closer to 40,000.