The application to the Attorney-General's Department claims that the church has about 2,000 adherents in W.A.
Mr Tampion has been told that his application is being considered.
But Federal officials today said there was no chance of it being granted.
The Federal government could hardly give official recognition to a representative of an organisation that at least one State, Victoria, was taking action to ban, they said.
The government itself was considering what action it should take against scientology in the A.C.T. and Northern Territory.
Legislation to ban Scientology is now before the Victorian parliament.
The Victorian government acted to ban the movement after Mr K. V. Anderson, QC, had reported that scientology was a perverted and dangerous form of psychology.
He said it was an evil practice with evil techniques.
Copies of the Anderson Report were sent to all States and have been under close examination in the Commonwealth Attorney-General's and Health departments.
Mr Tampion's application is for registration as a celebrant of marriages under the Marriage Act.
Under the act, the Commonwealth authorises nominated ministers of approved religions to conduct marriages.
The Attorney-General is also empowered to authorise other persons as celebrants of marriages.
He has exercised this power to register four ministers of the Bah'ai faith.
Mr Tampion's application says that the Church of Scientology was founded in the United States - in Washington and California.
Mr Tampion has also sought authority to conduct christenings and funerals but these matters are outside Federal jurisdiction.
In Perth yesterday, Mr Tampion said that he had performed six marriage ceremonies in the past two years.
To legalise their marriages the couples had been required to go through a Registry Office ceremony.
He had performed marriage ceremonies either in the chapel at the scientology headquarters at 263 Adelaide-terrace, at the home of one of the parties involved in the marriage, or at the wedding reception.
Mr Tampion said that adherents frequently used the term "group meetings" rather than "church services."
Scientology is to be discussed at three conferences of State and Federal ministers.
Health Minister MacKinnon said yesterday that the subject would be raised at meetings of attorneys-general and police and health ministers.
If legislative safeguards were considered necessary he hoped they could be prepared in time for next year's session of the State parliament.
He believed that measures taken by the States would need to be reasonably uniform to be effective.
He was anxious to see some control over hypnotherapy and psychotherapy, the categories in which scientology could fall.
The government intended to keep a watch on the activities of scientologists in this State.