A large fire on the only crossing between the occupied Crimean peninsula and Russia was caused by a lorry explosion, Russian officials say.
The blast on the road section then led to oil tankers on the rail section catching fire, with the road then collapsing.
Crimea was annexed in 2014 by Russia, which now uses the Kerch bridge to move military equipment into Ukraine.
Russian state media say traffic on the bridge has been suspended.
An adviser to Ukraine's President Zelensky, Mykhailo Podolyak, called the damage a "beginning" - but did not directly claim Ukrainian responsibility.
"Everything illegal must be destroyed, everything stolen must be returned to Ukraine, everything occupied by Russia must be expelled," he tweeted.
The official Twitter account of the Ukraine government responded to the fire by tweeting: "Sick burn."
Russia's National Anti-Terrorism Committee (NAC) said: "At 06:07 Moscow time today [03:07 GMT], an explosion was set off at a cargo vehicle on the motorway part of the Crimean bridge on the side of the Taman peninsula, which set fire to seven fuel tanks of a train that was en route to the Crimean peninsula.
"Two motorway sections of the bridge partially collapsed."
Crimean parliamentary speaker Vladimir Kontantinov blamed the explosion on "Ukrainian vandals, who have finally managed to reach their bloody hands to the Crimean bridge".
He added the damage to the bridge would be "promptly restored, since it is not of a serious nature".
Russian President Vladimir Putin has been briefed about the "emergency" on the bridge and has ordered a government inquiry, Kremlin spokesman Dmitry Peskov said, in comments quoted by Interfax news agency.
The 19km (12-mile) bridge across the Kerch Strait was opened by President Vladimir Putin in 2018, four years after Moscow illegally annexed Crimea.
It is said to be a key target for Ukrainian forces who have been attacking Russian logistics.
The crossing is more than 100 miles from Ukrainian-held territory. One explosives expert told the BBC said the fire was probably not caused by a missile.
"The lack of obvious blast / fragmentation damage on the road surface suggests that an air-delivered weapon was not used," he said
He said it was possible that "a well-planned attack from below may have been the cause".
"I suspect explosives on the road bridge and train deck were initiated near simultaneously using coded radio command," he said.
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