Energy markets have seen wild swings since the US and Israel attacked Iran on 28 February.
The US has intercepted an Iranian ship entering the Gulf as part of its naval blockade, US President Donald Trump has said.
Prosecutors say the singer, real name David Anthony Burke, could face life in prison due to the nature of the case.
The Israeli military says it views with "great severity" the actions of the soldier, as the US ambassador demands "swift" consequences.
