Ukraine says it has hit two landing ships, a communications centre and other infrastructure used by Russia’s Black Sea fleet off annexed Crimea.
An announcement by the Ukrainian general staff said the Yamal and Azov ships had been destroyed.
The Russian-installed governor of the port of Sevastopol said 10 Ukrainian missiles had been shot down.
Russia also launched a missile and drone attack on the capital, Kyiv, and the region of Lviv early on Sunday.
In an announcement, Mikhail Razvozhayev, the Russian-appointed mayor of Sevastopol, said damage had been caused to residential buildings and transport infrastructure as a result of the “massive” attack.
He asked residents not to publish information or any images.
UK Defence Secretary Grant Shapps praised the attack on the Russian ships, calling it a “historic moment for Ukraine”.
“In plain English, it means that Putin can no longer exercise safely in the Black Sea, even though the Russian Fleet has operated there since 1783,” Mr Shapps said.
He added that the world “cannot afford” for Ukraine to lose this war, and that the UK’s support for Kyiv in the face of Russian assaults “will remain undimmed”.
The BBC has not been able to verify the Ukrainian claim to have damaged the Russian landing ships, which are used to land troops and equipment straight to shore without the need for a pier or dock.
On Sunday morning, Kyiv residents took shelter in metro stations as the attack began at 05:00 (03:00 GMT).
Officials said their defences had shot down 18 Russian missiles and 25 drones there. There was only minor damage.
About 20 Russian missiles and seven drones targeted “critical infrastructure” in the western region of Lviv. No damage has been reported.
One of the cruise missiles entered the airspace of neighbouring Poland, a Nato member, the armed forces announced.
“The object entered Polish space near the town of Oserdow and stayed there for 39 seconds. During the entire flight, it was observed by military radar systems,” the armed forces said in a statement.
“If there was any premise indicating that this object was going in the direction of any targets located in Poland, of course, it would have been shot down and more adequate measures would have been taken,” Defence Minister Wladyslaw Kosiniak-Kamysz said.
Russia annexed Crimea in 2014 and launched a full-scale invasion of Ukraine in February 2022.
There has been an increase in aerial attacks by both sides in the past few days, even as Russia makes slow progress in taking some territory in the east of the country.
On Friday, Russia fired dozens of missiles at Ukraine, hitting a dam and leaving a million Ukrainians without power.
And Ukraine has been hitting targets in Crimea more regularly.
In particular, Ukraine has repeatedly hit the Black Sea fleet – seen as the best of Russia’s navy. Satellite images last year showed many of the Crimea-based warships had left the peninsula for the Russian Black Sea port of Novorossiysk.
Last month, the Russian landing ship Caesar Kunikov was sunk off the coast of Crimea, according to Ukraine’s armed forces.
Its sister ship Novocherkassk was hit while in port in Feodosiya in December last year.
In one of the biggest strikes on the Black Sea fleet, last September Ukraine attacked naval targets and port infrastructure, using as many as 10 missiles and three unmanned boats. It caused a large fire at a Sevastopol shipyard.
Ukraine’s biggest scalp in naval warfare has so far been the sinking of Russia’s flagship Black Sea missile cruiser, the Moskva, in April 2022.
Ukraine has also targeted the Kerch bridge several times, as it is an important resupply route for Russian forces occupying parts of the country’s south.
Kyiv has repeatedly said it plans to retake Crimea and all territories seized by Russia.
Ukraine is critically dependent on weapons supplies from the US and other Western allies to keep fighting Russia – a much bigger military force with an abundance of arms and artillery.