Israeli media showed badly damaged buildings in Arad, about 25 kilometres (15 miles) northeast of Dimona, a town struck hours earlier which houses a nuclear facility.

"In both Dimona and Arad, interceptors were launched that failed to hit the threats, resulting in two direct hits by ballistic missiles with warheads weighing hundreds of kilograms," firefighters said.

The local fire service said there was "extensive damage", with three buildings affected and a blaze sparked in one of them.

Magen David Adom first responders said they were taking 33 wounded people to hospital, including four seriously injured, 12 moderately injured, and 17 lightly injured.

"This is a very severe scene," emergency medical technician Yakir Talkar said in a statement, adding there were "many wounded with varying degrees of injury".

The casualties in Arad came after an Iranian missile strike on Dimona left around 30 people wounded.

Iranian state TV said the missile attack on Dimona in the Negev desert was a "response" to an earlier strike on its own nuclear site at Natanz.