Thousands of mourners today began the slow procession through City Hall security gates, past massive flower sprays and around the wooden caskets of murdered mayor George Moscone and supervisor Harvey Milk.

The man charged with the murders, former supervisor Dan White, appeared briefly in court this morning - silent, sober and wearing an orange prison jumpsuit - while Municipal Court Judge Robert J. Reynolds rescheduled arraignment for Dec. 6.

Gilbert Eisenberg, a lawyer appearing temporarily on behalf of White, said the delay has been requested because White's family had not yet settled on an attorney to represent him.

"Everyone is still in a state of shock," Eisenberg said.

Mayors from cities across the country - including Chicago, Syracuse, Los Angeles and Boston - were preparing to fly to San Francisco for Moscone's funeral Thursday afternoon, according to spokesmen in the mayor's office.

California Gov. Edmund G. (Jerry) Brown Jr., many members of Congress and Jack Watson, assistant to the president for intergovernmental relations, also have said they will attend the services. President Carter telephoned Mrs. Moscone Tuesday to express his sympathy, White House spokesmen said.

Moscone's funeral will be held in a large, modern cathedral about a mile from City Hall. The cathedral seats 5,000 but an overflow is expected, and the street outside will be wired for sound. Extensive security checks will be conducted on all mourners, the mayor's spokesmen said.

Security at the entrance to the courtroom where White appeared this morning was so extensive that each person entering the room - only members of the press were allowed in - was thoroughly frisked, led through a metal detector and asked to hand over any parcels or handbags for inspection.

This has been the case throughout City Hall since the double shooting Monday morning.

Police will not comment on increased security measures, but the number of armed officers stationed around the building has visibly increased, and employes entering the building are frequently being frisked, creating long lines at the entrance to City Hall.

This afternoon's procession past the casket began after an hour-long outdoor memorial service held on City Hall steps. An estimated 9,000 people gathered for the service, many in tears, particularly when Joan Baez and Carmen McRae stood to sing.

"In our sorrow," said actinf Mayor Diane Feinstein, "this lovely jewel of a city seems a dark and saddened place."

Friends of Harvey Milk said there will be no funeral for the slain supervisor. He will be honored at three memorial services this week, and on Thursday morning his body will be cremated. His ashes will be scattered at sea, as Milk had requested some time ago, friends said.