- The latest incident comes amid a much-anticipated counter-offensive by Ukrainian forces which aims to retake territory in southern and eastern Ukraine.
- The recent gains take the total area of reclaimed land to 210 sq km (81 sq miles) since the counter-offensive began.
Two people have died after an "attack" on the bridge linking the occupied Crimean Peninsula to Russia.
Moscow has blamed Ukraine for the incident, alleging US and UK involvement, but Kyiv has not officially said it was responsible.
The Kerch bridge was opened in 2018 and enables road and rail travel between Russia and Crimea - Ukrainian territory occupied by Moscow's forces since 2014.
Russia's transport ministry said the bridge's supports were not damaged.
The ministry said investigations were continuing, but unconfirmed reports said explosions were heard early on Monday.
Russian authorities have accused Ukraine of attacking the Kerch bridge with two "unmanned surface vessels" (USVs) - drones that travel over water rather than through the air.
As yet, the BBC not seen any visual evidence to confirm this.
But a source in Ukraine's security service has told BBC Russian it was behind the attack and that water-based drones were used.
Defence analyst Stuart Crawford said he thought drones had been used to attack the bridge's infrastructure.
In an interview with the BBC, Mr Crawford also said details around what happened would likely remain unclear as neither side would want to release too much information.
The alleged attack is the second major incident on the Kerch bridge in the past year. In October 2022, the bridge - which is an important supply route - was partially closed following a major explosion. It was fully reopened in February.
Monday's incident created long traffic jams on the remaining road route out of Crimea and severe train delays on the railway were reported. The ferry crossing that runs parallel to the bridge was also affected.
Russian officials urged holidaymakers stranded in Crimea to drive home through occupied Ukraine. They said they would reduce curfew times to let tourists through and that the Russian army would keep the route "safe".
Commercial flights between Russia and Crimea - a popular holiday destination for Russians since Moscow annexed it in 2014 - have been suspended since Moscow launched its full-scale invasion of Ukraine last year.
Vyacheslav Gladkov, governor of the western Russian region of Belgorod which is close to Russia's border with Ukraine, said in a Telegram statement that a Russian couple had died in Monday's incident. He added that their 14-year-old daughter had been injured.
Unverified photos posted by the spokesperson for the Odesa military administration of the alleged attack showed debris on the road across the bridge, as well as damaged railings.
Kremlin spokesman Dmitry Peskov said President Vladimir Putin had been briefed.
He added there was no connection between the incident and Russia's decision to suspend its participation in a United Nations-brokered agreement allowing Ukraine to ship out grain through the Black Sea.
Ukraine and Russia are among the world's top grain exporters, and the deal was reached amid fears that the war would lead to global food shortages, but Russia has so far refused to agree to an extension.
Russian foreign ministry spokeswoman Maria Zakharova accused Ukraine of attacking the Kerch bridge with the "direct participation" of the UK and the US, but provided no evidence to back up the assertions.
While a source within Ukrainian intelligence, the SBU, told the BBC it carried out the attack alongside the navy's special forces - there has been no open admission of responsibility.
However, the security services have hinted at Kyiv's role in the attack, saying in a statement that "all details regarding the explosion will be announced after the victory".
It is customary for the Ukrainian government to provide vague statements rather than claiming direct involvement.
The same bridge in Crimea was attacked last October. In the months before the incident, Ukrainian officials had repeatedly suggested that the bridge would be targeted - but in the days that followed Kyiv declined to claim responsibility. It was not until this month that a Ukrainian defence official admitted it was behind the operation. The BBC cannot independently verify the claims.
Even now, the exact cause of the explosion last October remains unclear. Footage from the time showed a huge fireball erupting as a number of cars and lorries made their way across the bridge.
The latest incident comes amid a much-anticipated counter-offensive by Ukrainian forces which aims to retake territory in southern and eastern Ukraine.
Ukraine's forces have retaken 18 sq km (7 sq miles) over the past week in their fightback, Ukraine's deputy defence minister Hanna Maliar said on messaging app Telegram.
The recent gains take the total area of reclaimed land to 210 sq km (81 sq miles) since the counter-offensive began.