KYIV (Reuters) -Russia attacked military and infrastructure targets across Ukraine early on Tuesday, including in the capital Kyiv and the western city of Lviv, Ukrainian officials said.

Ukraine said it had shot down 32 of 35 Iranian-made Shahed drones launched from Russia's Bryansk region and the Azov Sea.

But a "critically important facility" was struck in Lviv, far from the front lines and around 70 km (43 miles) from the border with NATO member Poland, regional governor Maksym Kozytskiy said. He gave no other details of the facility.

There was no mention of any casualties in the overnight air strikes, the latest carried out by Moscow since Kyiv began a counteroffensive in which it says it has recaptured 113 square km (44 square miles) of land from Russian forces.

The air force said on the Telegram messaging app that air defences had been in action in most regions of Ukraine.

"However, the main direction of attack by Iranian drones was the Kyiv region. More than two dozen Shaheds were destroyed here," it said.

President Volodymyr Zelenskiy's office said drones attacked the Kyiv region in several waves, with the air alert lasting for over four hours. Several commercial and administrative buildings and some private houses were damaged, it said.

The Energy Ministry said debris from falling drones damaged electricity lines in the Kyiv region and also in the Mykolaiv region in the south, cutting off electricity for hundreds of residents.

Air force spokesperson Yuriy Ihnat said in a radio interview that it was simply not possible for air defence systems to cover all of a country as large as Ukraine.

The air force said Russia had also hit the southeastern industrial city of Zaporizhzhia with Iskander and S-300 missiles.

Yuriy Malashko, head of the military administration of the Zaporizhzhia region, said Russia had targeted telecommunication infrastructure and agriculture and farming properties.

Ukraine's military said that, according to preliminary information, Russia had fired seven missiles at Zaporizhzhia.

The prosecutor's office said a 70-year-old woman was killed and three people wounded on Monday during a Russian artillery attack on the Sumy region in the northeast.

Reuters could not independently verify the reports. There was no immediate comment from Russia.

(Reporting by Olena Harmash in Kyiv and Lidia Kelly in Melbourne; Editing by Timothy Heritage)