Six construction workers were killed and several vehicles plunged into the river after the cargo ship crashed into the bridge.
The US president pauses the military operation to get ships through the Strait of Hormuz two days after he announced it.
Frank Gardner says it is not worth getting excited about the few ships passing through the Strait of Hormuz as the numbers are tiny compared to before February.
Frank Gardner discusses what we know about Trump's 'Project Freedom' in the Strait of Hormuz.
IRGC Naval Command said both a Greek-owned vessel called the Epaminondas and the Panama-flagged MSC Francesca had been seized.
Iranian state media have shared footage appearing to show forces boarding two cargo ships in the Strait of Hormuz.
Nations in the region have been keen to reach agreements as their economies are heavily reliant on Middle East energy.
The BBC's Orla Guerin travels to the edge of the critical waterway that Iran has put a stranglehold on.
It appears to be the first ship owned by a major European firm to go through the strait since the conflict began.