Russia annexed the Black Sea region in 2014 after a change of government in Ukraine, sparking fighting between Ukrainian forces and Russian-backed separatists in the country's east.
Ukraine says Russia's latest accusations are a pretext for more military threats.
In a video released by Russian media, men in military fatigues can be seen pulling what look like explosives, hand grenades and other devices from rucksacks laid out on the ground.
Russia says the items are among weapons its federal security agency, the FSB, seized in Crimea in an operation to intercept plans for armed attacks on the peninsula.
Russia says the operation also interrupted a Ukrainian spy network.
It says Ukrainian defence intelligence was responsible for two intended attacks on critical infrastructure to sabotage preparations for next month's parliamentary elections.
Russia says at least one Russian serviceman was killed in clashes that broke out during the operation, and it says arrests were made.
President Vladimir Putin has accused Ukraine of trying to provoke a new conflict and destabilise the peninsula.
He says Ukraine's government, elected after the removal of President Viktor Yanukovych in 2013, was opting to escalate tensions instead of choosing peace.
"This information is very worrying. It's true that our special services have thwarted an incursion into Crimea by the Ukrainian defence ministry subversive group. It looks like the people who seized power in Kiev and continue to hold it, instead of looking for compromise, have moved on to practising terror."
Ukraine president Petro Poroshenko has dismissed the accusations.
He says they are merely a pretext for more Russian military threats against his country.
His spokesman, Oleksandr Motuzyanyk, has told the BBC Russia's claims are nonsense.
"There are absolutely no grounds to accuse Ukraine of terrorist activity or, furthermore, to accuse Ukraine of having its sabotage groups in Crimea. This is absolute nonsense and does not correspond to the facts."
Russia incorporated the Crimean peninsula in early 2014 after a local referendum on the peninsula's territorial status.
Armed conflict soon broke out in eastern Ukraine between separatist groups allegedly supported by Russia and forces loyal to the Ukrainian government.
In response to Russia's alleged military involvement in Ukraine, the United States and the European Union introduced sanctions against both individuals and businesses.
Petro Poroshenko says Russia will not succeed in having those sanctions lifted by trying to discredit Ukraine.
He says he also expects Russia to help ensure the terms of a 2015 ceasefire agreement reached in the Belarusian capital Minsk are fulfilled.
Vladimir Putin says Ukraine is playing a dangerous game and there is no point in holding a new round of peace talks on the sidelines of a G-20 summit in China next month.
Fighting has recently intensified in eastern Ukraine amid reports Russia is increasing its military activity in northern Crimea.
Russia says security has been tightened on the peninsula, especially on the border with Ukraine.
