Bauza told Cadena SER radio that two other victims were local residents, including an elderly woman whose body was found in the basement of her house.
It is understood at least 10 people have been tragically killed after muddy water engulfed the town of Sant Llorenç des Cardassar when a river burst its banks.
The British Foreign Office says it's investigating reports that a British couple are among those people who've been killed.
Emergency services confirmed that there had been at least five deaths in total, adding that "several [people] are missing".
At least six people are believed to have died when torrential rainstorms deluged the town of Sant Llorenc, about 40 miles east of the capital, Palma, on Tuesday evening.
Spain's Prime Minister Pedro Sanchez and members of Parliament hold a minute of silence for the victims of heavy rains in the Spanish island of Mallorca at the start of a parliamentary session in Madrid, Spain, October 10, 2018.
Authorities said 80 soldiers and seven vehicles from the military's emergency unit had joined Wednesday more than 100 rescuers who had been working in the area overnight.
A sports centre - the Miguel Ángel Nadal sports centre in the town of Manacor - has opened its doors to give shelter to local people whose homes have been damaged.
According to the Spanish media, people on the island have been rescued from rooftops and trees as 20cm (8in) of rain fell in four hours.
The weather agency, AEMET, said more heavy rainfall is expected Wednesday in eastern and southern parts of the Iberian peninsula.
He was planning to travel to the area later on Wednesday, his office said.