The bus had been carrying 37 pupils and seven members of staff to the Zara Maeen hot springs area when it was washed away, officials said.
"IDF soldiers searched for the missing in Jordan until the harsh weather made it impossible to do so and the Jordanian authorities called off the search", it said in a statement.
"I and all Jordanians are also bereaved by this tragedy", His Majesty said, adding that the tragedy touched the hearts of people in the region and around the world, who expressed their solidarity with Jordan. -Gen. Farid al Sharaa told state television.
Roads leading to the area were closed on Friday morning "to allow search and rescue operations", the Directorate of General Security said.
Late Thursday, 10 more students and a teacher were located and awaiting rescue, media reports said.
"[The floodwaters] swept away the students for 4 to 5 kilometers [2-3 miles]", Brig.
The Jordanian government launched investigations into the field trip organised by an Amman private school to a Dead Sea valley on Thursday despite official warnings of heavy rains forecast to hit the kingdom.
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A complex rescue operation involving helicopters, divers, sniffer dogs and hundreds of searchers had continued into the night Thursday and then resumed after daybreak on Friday.
King Abdullah II of Jordan, said that the Dead Sea flood incident "was a great tragedy that hurt all of us as Jordanians, God bless the dead and give us patience".
Israel's military said it dispatched helicopters from the elite search-and-rescue Unit 669 at the request of the Jordanian government.
Jordan's state news agency, Petra, confirmed the death toll in a tweet, saying dozens more had been rescued.
Flash flooding was reported in the south due to heavy rainfall with police closing off Highway 90 by the Dead Sea, which flooded it.
Civil defence spokesman Capt. Iyad al Omar told Reuters the number of casualties was expected to rise.