Authorities say that 61 rebels have been killed, but 12 police and 12 civilians also died in the assault on Nalchik in Kabardino-Balkaria province.
Officials say militants are holding hostages at a police station in the city, which has been sealed off.
Militants from nearby Chechnya are believed to be behind the attacks.
A pro-rebel website said a group known as the Caucasus Front had claimed the attack.
The raid is the latest in a series of disturbances that have been destabilising Russia's North Caucasus for more than a year.
Nalchik is about 100 km (60 miles) north-west of Beslan, where Chechen rebels took hundreds of hostages at a school in 2004, in an attack claimed by warlord Shamil Basayev.
'Find the bandits'
Dozens of men armed with rocket launchers are said to have been involved in the fighting which broke out early on Thursday.
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The BBC's Emma Simpson in Moscow says this appears to have been an all-out attack on Nalchik's law enforcement and security services.
A local Interior Ministry source told Itar-Tass that rebels launched a "carefully planned" simultaneous attack on police stations, security forces, military and drugs-control offices and the airport.
"All hell broke loose, and the impression was that there was shooting everywhere," a resident told Reuters news agency.
A school was also caught up in the running gun-battles, as black smoke billowed across the city.
President Vladimir Putin responded with an order for the city to be sealed off and for forces to shoot any armed resisters.
Officials said two small groups of fighters were holed up in a police station and a shop and were holding small numbers of hostages, but there was no shooting elsewhere.
Deputy Interior Minister Andrei Novikov told reporters that 61 militants had been killed.
"The city has been taken under firm control. Not one car, not one train, not one bus will go past without being closely checked," Deputy Interior Minister Alexander Chekalin said.
"Now our main task is to find the bandits in the city, including their wounded."
Website claim
The pro-rebel Kavkaz Center website said that a detachment of the Chechen-linked Kabardino-Balkaria jamaat, called Yarmuk, had entered Nalchik.
Gunfire was heard throughout the city
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The use of the word jamaat indicates that it is made up of radical Islamic fighters.
Correspondents say violence in Kabardino-Balkaria has been steadily increasing.
Political changes and a harsh crackdown on alleged Islamic militants appear to have pushed the region to the verge of instability, the BBC's regional analyst Steven Eke says.
Our analyst says that after last year's Beslan massacre the government promised more money and support for the impoverished North Caucasus - but nothing has changed.
Have you been affected by the clashes in Nalchik? Do you live in the city? Do you have families and friends who may have been caught up in the violence? Send us your experiences. If you have any still pictures or moving images you can send them to yourpics@bbc.co.uk.