The four puppies were trapped under debris in the same room as a fire.
Fire and Rescue Commissioner Eyal Caspi signed an order prohibiting the lighting of bonfires and fires in open areas.
Keren Kayemet L'Israel (KKL-JNF) forestry teams and Israel's Fire and Rescue Services fought at least 176 separate forest fires across Israel last Saturday.
The exercise was carried out with the aim to enhance response capabilities for the upcoming summer, amid growing risk associated with climate change and the potential for large-scale wildfires.
The fire began on Monday near Kibbutz Kalia, north of Israel's Dead Sea.
Thirteen injured people with varying degrees of injury, three of which were in moderate condition, were evacuated to medical centers in Haifa.
Four major fires broke out across Israel on Monday, with dozens of firefighting teams and multiple planes fighting against the flames.
The children from the Israeli Bedouin town of Tel Sheva were hurried to the hospital in serious condition but died there shortly after.
No foul play was suspected.
Firefighters were continuing to tackle the blaze and 80 people have been evacuated, according to the rescue services.
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