The fighting was some of the fiercest in recent months
Argun has been under blockade since Thursday as the Russians search for separatist rebels.
Some of the rebels are believed to have fled another Russian operation in the nearby village of Tsotsin-Yurt.
Reports say that a fierce firefight began on the outskirts of Argun, 15 kilometres (9.5 miles) east of the republic's capital, Grozny, after rebels fired from two sides of a bridge at a Russian patrol that was crossing into the town.
Russian tanks and helicopter gunships bombarded the area.
The fighting was some of the fiercest seen in Chechnya in recent months.
New year security
A spokesman for the Chechen rebel leader, Aslan Maskhadov, said a number of civilians had been killed or wounded in the blockade and search operation in Argun.
Russian forces had killed four citizens and rounded up 150, a Chechen website, Kavkaz Center, reported.
Russian troops continued their sweep on Monday, seizing 13 people suspected of taking part in rebel action, the Interfax news agency reported.
Russia sealed off several Chechen areas, including Argun, as part of security operations ahead of the new year celebrations.
Other areas shelled
The army also shelled bases in three other districts of southern Chechnya, killing four rebels, an official in the Moscow-backed Chechnya administration told The Associated Press news agency.
The army said its forces had recently killed more than 100 rebels in areas east and south-east of Grozny, while the rebels say they have killed 40 Russian soldiers and injured about 40.
Chechen separatists won de facto independence after a 1994-96 war that ended with a Russian withdrawal, but Moscow sent troops back into the breakaway republic in October 1999.
The protracted guerrilla war has already claimed tens of thousands of lives.