Mr. Johnson’s case has drawn attention to a pattern of homophobia-driven crimes in the 1980s and ’90s in which gay men were targeted by gangs of young people, who sometimes forced them off cliffs to their deaths. Former officials have acknowledged that the deaths were not adequately investigated at the time by police officers, many of whom had a reputation for hostility toward gay men.

The new reward, the equivalent of about $720,000, is a tenfold increase from the previous one. The police say they hope it will motivate people to share information.

“Scott’s death is possibly one of the most challenging investigations I’ve seen — and it’s believed one of the greatest hindrances has been an unwillingness for witnesses to come forward,” said Mick Fuller, the police commissioner for the state of New South Wales, which includes Sydney.

Mr. Johnson’s brother, Steve Johnson, who flew into Sydney for the announcement, said the reward was an “incredible step” toward answers.

“I’m very encouraged,” he said in a phone interview on Sunday. “The million-dollar reward is speaking to the community that the police are taking this seriously and they need people’s help.”