The Russian president has convened an urgent meeting of his country's security council on Monday to discuss the explosion.
Senior Russian leaders will meet on Monday for a hastily-arranged Security Council session, to discuss the country's response to a weekend bridge explosion in Crimea.
In a Sunday night video, Vladimir Putin said "there is no doubt. This is an act of terrorism aimed at destroying critically important civilian infrastructure."
"This was devised, carried out and ordered by the Ukraine special services," he added.
Saturday's explosion tore through a bridge linking Crimea with Russia. The bridge was opened in 2018, and is an imposing symbol of Moscow's illegal annexation of the Ukrainian peninsula.
Security Council Deputy Chairman Dmitry Medvedev said ahead of Monday's meeting that Russia should kill the "terrorists" responsible for the attack.
"Russia can only respond to this crime by directly killing terrorists, as is the custom elsewhere in the world. This is what Russian citizens expect," he was quoted as saying by Russia's state news agency Tass.
The bridge over the Kerch Strait, Europe's longest, is a major supply route for Moscow's forces in southern Ukraine, and is also a vital artery for the port of Sevastopol, where the Russian Black Sea fleet is based.
Images showed part of the bridge's roadway blown away, although rail services and partial road traffic resumed.
The Russian transport ministry, quoted by RIA news agency, said nearly 1,500 people and 162 heavy cargoes had travelled by ferry across the Kerch Strait since the explosion.
Russia's defence ministry said its forces in southern Ukraine could be "fully supplied" through existing land and sea routes.
On Sunday, Putin met with Alexander Bastrykin, the head of Russia's Investigative Committee, who presented findings of an inquiry into what he said was the explosion of a vehicle and subsequent fire on the bridge.
Bastrykin said the vehicle had travelled through Bulgaria, Georgia, Armenia, North Ossetia and Russia's Krasnodar region before reaching the bridge. Among those who helped Ukrainian special services prepare were "citizens of Russia and foreign countries," Bastrykin added in the video on the Kremlin's Telegram channel.
Ukrainian response to 'terrorism' accusation
In Kyiv, presidential adviser Mikhail Podolyak called Putin's accusation of terrorism “too cynical even for Russia.”
“Putin accuses Ukraine of terrorism?" he said. "It has not even been 24 hours since Russian planes fired 12 rockets into a residential area of Zaporizhzhia, killing 13 people and injuring more than 50. No, there is only one state terrorist and the whole world knows who he is.”
Podolyak referred to missile strikes on the city of Zaporizhzhia overnight that brought down part of a large apartment building. The six missiles were launched from Russian-occupied areas of the Zaporizhzhia region, the Ukrainian air force said.
The region is one of four Russia claimed as its own this month, though its capital of the same name remains under Ukrainian control.