One naval drone was destroyed late Friday and two others early Saturday morning, according to Russia's Defense Ministry. There was no immediate comment from Ukrainian officials.
The Kerch bridge, which is a key supply route for Kremlin forces in Russia's war with Ukraine, has come under repeated attack since Russia launched its full-scale invasion.
An explosion in October, which Russian authorities said was caused by a truck bomb, left three people dead. A further attack on the bridge in July, killing a couple and seriously wounding their daughter, left a span of the roadway hanging perilously.
The bridge connecting Crimea and Russia carries heavy significance for Moscow, both logistically and psychologically, as a key artery for military and civilian supplies and as an assertion of Kremlin control of the peninsula it annexed in 2014.
On Saturday afternoon, one civilian was killed and two wounded during shelling of Russia's Belgorod region bordering Ukraine, Belgorod Governor Vyacheslav Gladkov said.
Two Ukrainian drones attacked the region's Valuysky district, causing minor damage to a private home and car, while another drone was intercepted by Russian air defence in the Grayvoronsky district.
A woman was also wounded Saturday during shelling of a village in the neighbouring Kursk region, also bordering Ukraine, regional Governor Roman Starovoit said. He blamed Ukraine for the shelling.
Ukrainian authorities, which generally avoid commenting on attacks on Russian soil, didn't say whether they launched the attacks. Drone strikes and shelling on the Russian border regions are a regular occurrence.
Meanwhile, four people were wounded in the Ukrainian shelling of the eastern Ukrainian city of Donetsk, Moscow-installed mayor Aleksei Kulemzin said Saturday.
Donetsk is the regional capital of the eastern Ukrainian province of the same name, which was among the four Ukrainian provinces illegally annexed by Russia in September. The city came under the control of Russia-backed separatists in 2014.
The Ukrainian military said in a regular update Saturday that over the previous 24 hours, Russia had launched four missile strikes and 39 air strikes, in addition to 42 attacks from multiple rocket launchers.
One person was killed and two were wounded during shelling of Ukraine's southern Kherson region on Saturday, according to Governor Oleh Prokudin. Farther north, a 32-year-old police investigator was killed and two other people were wounded when shells hit the town of Seredyna-Buda in the northeastern Sumy region.
Four people were wounded during artillery shelling and drone attacks in the Nikopol district of the Dnipropetrovsk region, according to regional Governor Serhii Lysak. Elsewhere in the province, Kryvyi Rih Mayor Oleksandr Vilkul said the anti-aircraft defence in the central Ukrainian city, which is President Volodymyr Zelenskyy's hometown, had successfully thwarted a strike, without specifying the nature of the attack.
A missile hit an apartment on the first floor of a multistorey building in the eastern city of Kramatorsk but there were no casualties, Donetsk regional Governor Pavlo Kyrylenko said.
UK military officials said Saturday that Russia risks splitting its forces in an attempt to prevent a Ukrainian breakthrough in Ukraine's south. According to British intelligence, Ukrainian forces continued to take offensive action on the Orikhiv axis in southern Ukraine, with units reaching the first Russian main defensive line.
Zelenskyy said Saturday that Ukrainian forces were "on the move," after Ukrainian Deputy Defense Minister Hanna Maliar announced Friday that Kyiv's troops were advancing in the Zaporizhzhia region.
