Russia and Ukraine trade blows in the south.

MYKOLAIV, Ukraine — Ukrainian and Russian forces traded long-distance blows in southern Ukraine on Friday, bombing each other’s positions and inflicting major damage.

The two top floors of the city administration building in Kherson, a southern Ukrainian city the Russians occupy, were turned into rubble by a Ukrainian missile strike. At least three people died, according to the Russian news agency TASS. The Ukrainians took credit for the attack, saying it was an attempt to decapitate the leadership of the occupied area.

“All the collaborators of the occupied Kherson region were gathered there,” said Serhiy Khlan, a regional legislator. “When they all gathered, a ‘greetings’ from the Armed Forces of Ukraine arrived.”

Mr. Khlan warned civilians to stay away from government offices and military targets in Kherson, in case there are more strikes.

In Kryvyi Rih, a Ukrainian industrial city under government control, the Russians hit a gigantic dam for the third consecutive day on Friday, damaging it but not causing any serious flooding. Ukrainian officials have said that the Russians are trying to breach the dam, sending torrents of water downstream, to frustrate the efforts of Ukrainian forces to cross the river.

Natalia Humeniuk, the spokeswoman for Ukraine’s southern military command, said the attacks on critical infrastructure facilities signified a new stage of hostilities in the seven-month war.

The attacks are “not only for direct damage,” she said on Friday. “It also creates insane psychological and social pressure, as we are approaching the winter.”