As the death toll continued to mount from yesterday's dam disaster in Italy's northern Alps, the government of Prime Minister Bettino Craxi today ordered a full government investigation of the catastrophe that has revived concerns about lax safety controls on Italy's industries.

The investigation was decided upon as 5,000 rescue workers dug through tons of mud that washed through two mountain towns in the Val di Fiemme in the Italian Dolomites. Authorities announced that to date 170 bodies had been recovered, one injured person had died in a hospital and another 24 persons were missing and presumed dead.

The government decision came after a five-hour emergency Cabinet meeting that dealt both with the tragedy in the once beautiful Val di Fiemme and with the government's financial crisis following the collapse in the value of the Italian lira yesterday.

Speaking to journalists after the Cabinet meeting, Deputy Prime Minister Arnaldo Forlani made it clear that the government investigation would seek to establish whether individuals or officials were in any way negligent with regard to the construction, maintenance and checking of the small dirt dam, owned by a fluorite mining company, that burst, sending mud and rock onto residents and tourists in the Val di Fiemme yesterday.

Trento State Prosecutor Francesco Simeoni notified the owners of the Prealpi Mining Co. of Bergamo that they are under investigation on possible charges of multiple manslaughter and causing an unpremeditated disaster, United Press International reported.

Simeoni questioned Giulio Rota, coowner of the firm with his brother Aldo.

Giulio Rota emerged from the session and told reporters he believed the disaster "was caused by the infiltration of rain that occurred in the last few days."

Offers of help poured in from around the world, including from the governments of the United States, France, Britain, West Germany and Japan.

The dam, which had served as a collection and filtration pool for waters from the mine, sent a three-mile tongue of mud, silt and rock rushing down the valley, wiping out the hamlet of Stava and damaging parts of the town of Tesero. At least three small hotels were destroyed along with dozens of houses.

Val di Fiemme residents today told journalists they had complained about the construction of the dirt dam above their villages but that the dam had been built anyway and their complaints and fears were ignored.

National concern about establishing who might be guilty of irresponsibility or negligence in the dam's construction and inspection was underlined by extensive press and official recollections today of another tragedy in 1963 when a landslide and flood near Longarone, in the Alps to the east of the Val di Fiemme, killed more than 2,000 people.

Two engineers convicted in connection with that accident received jail sentences of eight months and two years.