The official news agency Petra said that rescue work continues to remove the 43 students and teachers who were on the bus in the area of the hot springs of Al Zahra, between Wadi Mujib and Wadi Zerka, on the shores of the Dead Sea, Efe reported.
Most of the children killed in the incident were below 14.
The Israeli military said on Thursday it was helping with the operation, sending helicopters and forces specialised in search and rescue.
Razzaz said divers and civil defence search teams would be conducting search operations deep inside the Dead Sea throughout the night.
They had been on an outing with chaperones when, according to a witness, floodwater swept their bus into a valley.
Thirteen people escaped the flooding without injuries, with some holding on to rocks to survive.
Thirty-four people were rescued in a major operation involving police helicopters and hundreds of army troops, police chief Brigadier General Farid al Sharaa told state television.
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Jordanian Prime Minister Omar Razzaz sent his condolences to the families of the victims, promising an investigation into the incident, and said that anyone responsible would be held accountable.
Late on Thursday, 10 more students and a teacher were found and awaiting rescue, media reports said.
"The number of those killed in the flash flood is expected to increase because many were reported to have been swept away by the raging water", the official said.
Later on his Twitter account, he appeared to suggest there had been something amiss in the school's application to run the trip. The arid region, the world's lowest point at about 1,400ft (430m) below sea level, is often hit by flash floods.
The low-lying Dead Sea area is prone to flash flooding when rain water rushes down from adjacent hills.
As the death toll continued to rise Thursday evening, Jordan's King Abdullah II announced that he had cancelled a visit to Bahrain, which had been scheduled for Friday.