Deborah Thomas, CEO of Ardent Leisure, which owns the Dreamworld theme park in Queensland, Australia, said in a statement that she would donate her annual bonus of AUS $167,500 ($127,672) to the Red Cross to "support people affected by this tragic event."
She said that she has been "deeply affected and saddened by the tragic deaths," especially because of "the impact of this incident on their children and families."
Separately, Ardent Leisure said in a statement it would be "offering the victims' families support through the Queensland police liaison office and this includes financial support."
Six people were riding a "flume" on the park's Thunder River Rapids Ride when the incident happened. Their flume flipped after it came in contact with another carriage towards the end of the ride, tossing some of the passengers onto a conveyor belt, where they were caught in the machinery, police said.
'Shock and mourning'
The brother of one of the four victims said his family is in "shock and mourning."
Simon Araghi confirmed that Roozbeh Araghi, known as Roozi, died in the accident with his partner Luke Dorsett and Dorsett's sister, Kate Goodchild.
"On behalf of my brother Dory and my family, I confirm the loss of our most loved 'baby' brother Roozi and his partner Luke and our lovely Kate," Araghi wrote. "We appreciate all your support and would prefer to keep some privacy. We are all in shock and mourning."
The fourth victim was Cindy Low, a New Zealand citizen and long-term resident of Australia, whose 10-year-old son survived the fatal accident, according to a statement from a company hired to represent the family.
"The family are traumatized, and kindly request their privacy be respected as they try to come to terms with this tragic loss," the statement said.
All the victims were in their 30s and 40s.
Dreamworld earlier released a statement that, under advice from the Queensland Police Services, the park will not proceed with a memorial planned for Friday.
"The integrity of the Coronial Investigation is of paramount importance and postponing the service will give QPS the time it needs to conduct this investigation," the statement reads.
An earlier statement from Dreamworld PR had said a "private ceremony" would be held for staff, friends and the emergency services Friday.
Updated plans for a service, and the park's reopening, will be released Monday, the statement adds.
Low's son was one of two children who survived when the flume, carrying six people, "flipped" on the Thunder River Rapids Ride on Tuesday.
Brian Codd, assistant commissioner for Southeast Region of Queensland Police Service, described it as "almost a miracle" that the boy and a girl, aged 12, were able to "extricate themselves."
The ongoing accident investigation is "intricate" and "very complex," according to Detective Inspector Mark Thompson, with the Queensland Police at the Gold Coast Criminal Investigation Branch.
Thompson said an investigation center had been set up, and that police had taken more than 40 statements. He appealed for anyone who might have been on the ride that day or have relevant photos or mobile phone footage to get in touch.
Thirty detectives and a "significant number of scientific police" and workplace safety experts are investigating the incident, Thompson said, as he cautioned that it would be a "lengthy process."
'Extraordinary loss' for children
"In particular, we would like to acknowledge the tragic circumstances and extraordinary loss for their children," he said.
Dreamworld also also sought to defend the park's safety procedures in the statement, saying that the park was "fully compliant with all required safety certifications.
The attraction, in Gold Coast, about 45 minutes from Brisbane, is the largest theme park in Australia and attracts around 1.8 million visitors each year. It includes animal attractions and more than 50 rides, according to its owner, Ardent Leisure.