It was not immediately clear how the bridge, one of President Vladimir Putin's prestige projects, was attacked but video posted on social media showed the family's car smashed, with bloodied bodies contorted and silent.

As other drivers try to give assistance, a girl can be heard crying and whimpering.

Blood seeps from the door into a puddle on the road as one of the other drivers implores the girl to keep still.

The girl was named as 14-year-old Angelina. Her parents, Alexei and Nataliya, both died.

"The girl was injured," Vyacheslav Gladkov, governor of the Belgorod region, said on the Telegram messaging app. "The hardest thing is that her parents died - dad and mum."

"No words can soothe the pain of loss here," he said. The car they had been travelling in was from the Belgorod region, one of the Russian border regions that has seen the conflict in neighbouring Ukraine spill across the frontier.

Russia's Investigative Committee said Kyiv was behind the attack and opened a terrorism case.

Ukraine's military suggested Russia was responsible but Ukrainian media said Ukrainian security services had used - underwater drones to attack the bridge - which had only recently returned to full operation after suffering severe damage in a similar attack last October.

"Two civilians were killed - a man and a woman driving a car on the bridge. Their daughter, a minor, was injured," the Committee said.

The girl sustained injuries to her head and chest but was conscious and breathing independently and her life was not in danger, according to the local emergency response headquarters, which said psychologists were on hand.

Russian media said the family had been on their way to a holiday in Crimea, which Russia seized and unilaterally annexed from Ukraine in 2014.

Western sanctions imposed over the war in Ukraine have made it much harder and more expensive for Russians to travel to Europe, limiting their options for summer holidays.

An unidentified relative told the RBK news outlet that the family had been travelling with the girl's aunt, in two cars, and decided to drive at night to avoid traffic jams.

"At about 3 o'clock in the morning, the family heard the first bang, after which the lights went out on the bridge," the relative said.

"After the second bang, there was no more contact."

(Reporting by Guy Faulconbridge in Moscow and Lidia Kelly in Melbourne; Editing by Kevin Liffey)

By Guy Faulconbridge