A man later rang a friend of Ms Blackman's to say she had joined a cult and would not be returning. Reports in Japan say the call was traced to the suspect's mobile phone.
Tim Blackman, 47, who is back in Japan for the first time since the arrest last month of a possible suspect, said he wanted to make an international appeal to hostesses who might have been assaulted by the man and have since left Japan.
His 22-year-old daughter went missing on 1 July after saying she was going on a day trip with an unidentified customer from the Tokyo bar where she worked.
A man later rang a friend of Ms Blackman's to say she had joined a cult and would not be returning. Reports in Japan say the call was traced to the suspect's mobile phone.
Other theories about her disappearance include claims she may have been abducted as part of an illegal Hong Kong sex trade or kidnapped by an infatuated customer.
Arrest
The police arrested a 48-year-old Japanese businessman, Joji Obara, last month.
He is charged with raping two Canadian bar hostesses, but police have found no direct connection with Miss Blackman's disappearance.
After weeks of questioning, Mr Obara admitted he did meet her at the bar where she worked shortly before she went missing, but denied harming her.
The BBC's Charles Scanlon in Tokyo says police have recovered hundreds of videos showing Mr Obara having sex with foreign women.
At least three other cases involving sexual assaults on blonde foreign women - including two Australians and a New Zealander - are being followed up by the police in Tokyo.
Mr Blackman, a property developer from Ryde, Isle of Wight, has made a number of emotional appeals for help from the Japanese public during frequent visits to Tokyo.
More than 30,000 leaflets with Miss Blackman's photograph on have been distributed around Tokyo, and her family has put up a £10,000 reward for information leading to her discovery.
The family also set up a hotline in Tokyo and private investigators from both Britain and Japan have joined the search.