The letter has been turned over to the FBI's Joint Terrorism Task Force for testing and investigation.
It was unclear how the letter intercepted by the White House facility was similar to the ricin-laced ones addressed to Bloomberg.
Two threatening letters postmarked in Louisiana and containing traces of the deadly poison ricin were sent to Bloomberg in New York and to his gun-control group in Washington, officials said.
The anonymous letters were opened in New York on Friday at the city's mail facility in Manhattan and in Washington on Sunday at an office used by Mayors Against Illegal Guns, the nonprofit started by Bloomberg, police said Wednesday.
Police said preliminary testing indicated the presence of ricin in both letters involving Bloomberg, but that more testing would be done. Police said the threats contained references to the debate on gun laws and an oily pinkish-orange substance..
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