A service spokesman, Cmdr. Conrad Chun, said the Navy was awaiting further rounds of testing before reaching a definite conclusion.
A federal law enforcement official also said tests by late Friday had "come out negative" and further results were due Saturday afternoon.
Both the FBI and Homeland say they are awaiting the results of one final "culture" test. That answer will not be available until tomorrow, reports CBS News Correspondent Bob Orr.
But, as one DHS official puts it, "it's a 98% certainty at this point that we're not dealing with anthrax."
Officials closed the Navy mail-sorting offices and 11 other post offices in and around Washington Thursday after an automated alarm and one follow-up test indicated the possible presence of anthrax spores at Anacostia Naval Station.
The post office said it was reopening two of the 11 closed offices Friday night and the remainder would be back in service Saturday.
Officials have not located any contaminated mail.
The five workers were being offered the antibiotic ciprofloxacin as a precaution recommended by the Centers for Disease Control and Prevention, said the Navy spokesman, Chun.
An earlier follow-up test Thursday indicated 138 anthrax spores were present, Chun said, but it was not clear whether they were live spores.
Preliminary tests for anthrax often are inaccurate and there have been several false alarms since the still-unsolved anthrax attacks in 2001.
The anthrax-by-mail incidents in late 2001 showed that inhaling only a few spores, in some cases, was enough to infect some people with the deadly disease. Five people died in those attacks, which also forced the shutdown and cleanup of postal facilities in Washington and elsewhere.