The blasts on Tuesday engulfed an ammunition depot at a military base in the north of the Crimean peninsula, disrupting trains and forcing the evacuation of 2000 people from a nearby village, according to Russian officials and news agencies.
Plumes of smoke were later seen at a second Russian military base in central Crimea, Russia's Kommersant newspaper said. The action followed explosions at a Russian military air base in western Crimea last week that destroyed eight warplanes.
Russia's defence ministry said Tuesday's explosions at the ammunition depot were "a result of sabotage". The Crimean peninsula, which Moscow annexed in 2014, is the main supply route for Russian forces in southern Ukraine and the base for its Black Sea fleet.
Ukraine did not confirm or deny responsibility for the explosions though its officials openly cheered Russia's setbacks there.
As Kyiv considers a potential counter-offensive in the south, the explosions raised the prospect of new dynamics in the six-month-old war if Ukraine now has capability to strike deeper in Russian-occupied territory or pro-Kyiv groups are having success with guerrilla-style attacks.
President Volodymyr Zelenskiy urged Ukrainians to steer clear of Russian military bases and ammunition stores and said the explosions could have a number of causes, including incompetence.
"But they all mean the same thing - the destruction of the occupiers' logistics, their ammunition, military and other equipment, and command posts, saves the lives of our people," he said in an evening address.
Attention has also focused in recent days on shelling near the Zaporizhzhia nuclear reactor complex, Europe's largest, in a Russian-occupied area of southeastern Ukraine.
Russian-installed officials there, quoted by Interfax news agency, said on Tuesday Ukrainian forces shelled the city of Enerhodar where the plant is located. They accused Ukraine of doing so to provoke Russia into returning fire.
Later on Tuesday, 20 Russian rockets and 10 artillery rounds hit the city of Nikopol on the Ukrainian government-controlled bank of the Dnipro river across from Enerhodar, the Ukrainian regional governor Valentyn Reznichenko wrote on Telegram.
He said four people were wounded.
Reuters could not immediately verify either side's accounts.
Each side has blamed the other for heightened risks to the Zaporizhzhia plant, which Russia seized in March, though Ukrainian technicians continue to operate it.
The Ukraine conflict has caused millions to flee, killed thousands and deepened a geopolitical rift between the West and Moscow, which calls its invasion a "special military operation" to demilitarise its neighbour and protect Russian-speaking communities.Â
Ukraine, which was part of the Russian-dominated Soviet Union until its 1991 break-up, accuses Russia of waging an imperial-style war of conquest.
