MOSCOW — Islamic militants infiltrated Grozny, the capital of Chechnya, overnight and early Thursday, seizing buildings and opening fire on security forces in a gun battle that killed 10 police officers and nine militants, officials said. The attack came just hours before President Vladimir V. Putin delivered a state of the nation speech in Moscow, in which he made only a passing reference to the violence.

The Russian state news media reported that the militants had seized an office building, which was then recaptured by security forces, and a school. Terrified residents of Grozny said they heard loud explosions and saw armed gunmen roaming the streets.

Andrey Chatsky, a spokesman for Russia’s National Antiterrorist Committee, confirmed in a statement broadcast on Russian television that 10 police officers had been killed and 28 injured in the clashes.

Ramzan A. Kadyrov, the head of the Chechen Republic, said in a statement posted on his website, “We have the corpses of nine militants.” Earlier, he told the news agency Interfax that the office building, called the House of Publishing and used by newspapers and other media, had been recaptured by morning, and that all seven militants inside had been killed.

Mr. Kadyrov did not say whether there were any civilian casualties. The Interior Ministry for the Chechen Republic did not answer telephone calls on Thursday evening.

The attack ended a period of relative stability in Chechnya and other largely Muslim regions of southern Russia. In his speech, Mr. Putin said Russia was able to face the threat from terrorist attacks like the one in Grozny.

Residents of Grozny reached by telephone said the militants had a wider list of targets, and spoke of broader mayhem in the city.

As dawn broke, smoke was rising from several locations, they said.

“Oh God,” one man said in a video posted online, which shows shaky, silhouetted figures of armed men. “Fighters are on the streets.”

The Interfax report quoted Mr. Kadyrov as saying that civilian victims of the violence would be compensated, without indicating how many had been wounded or killed, or whether the gunmen had taken hostages.

Fighting at a nearby school, School No. 20, where militants had holed up overnight, had subsided by Thursday evening Mr. Kadyrov said.

On his Instagram account, Mr. Kadyrov advised residents of neighborhoods in the center of the city to remain at home and away from windows.

Residents described explosions from heavy weapons, either tanks or artillery, in several parts of the city. Kheda Saratova, a human-rights activist, said in a telephone interview that gunfire broke out around 1 a.m. and continued through the morning.

Varvara Pakhomenko, an independent analyst of the region, said residents were reporting gunfire in many locations.

Gunfire broke out near Rosa Luxemburg Street, a thoroughfare in the city that runs parallel to Vladimir Putin Street, in addition to the House of Publishing and School No. 20, she said.

“This could be a symbolic attack to show they can still organize something significant,” Ms. Pakhomenko said, referring to the Islamic militants. “They need new supporters and new fighters.” Many Muslims from Chechnya and Dagestan, another republic in southern Russia, have gone to to Syria to join the fight against President Bashar al-Assad.

Islamic fighters in southern Russia are organized as the Caucasus Emirate, a religiously motivated and pan-Caucasian movement that evolved from the initial Chechen nationalist and secular struggle for independence in the 1990s. Thursday is close to the 20th anniversary of the start of the first Chechen war.

While many Chechens fight alongside the Islamic State, the main militant group in Iraq and Syria, the leader of the Caucasus Emirate, Aliaskhab Kebekov, is not known to have sworn allegiance to the Islamic State.

In a television interview in Moscow, Mr. Kadyrov bragged that he had time to personally manage the counterterrorist operation in Grozny and still attend Mr. Putin’s speech.

“When this all started,” he said, “I flew home, held a special operation, killed the devils, held a meeting, gathered the staff for restoring the damaged building and made it in time to listen to the address of our national leader, the president, Commander in Chief Vladimir Putin.”