The discovery in the mail room of the Ford Office Building marked the first time evidence had been found on the House side of the complex.
But our correspondent says that there is some suspicion that this may not be evidence of a separate delivery of anthrax.
The post for both the House and the Senate goes to the same place before it is forwarded to the two bodies' mail room.
Click here to see where anthrax has been discovered
The police suggested that there was a possibility of cross-contamination from the envelope that was delivered to Mr Daschle.
But they cautioned that they needed to investigate further.
Workers in the Ford building are being tested for exposure to anthrax.
The discovery came as the United States Federal Bureau of Investigation said it had
tracked two anthrax-bearing letters to a post office sorting box in New Jersey.
Anthrax match
US Homeland Security Chief Tom Ridge said that the strain of anthrax used in the attacks on US media companies and the Senate appeared to be the same.
"We are obviously preparing for more," he said, though the FBI were unable to provide further details about the New Jersey investigation.
On Friday, a postal worker in the state became the eighth person to be diagnosed with an anthrax infection.
"The tests to date have concluded that the strains are indistinguishable," Mr Ridge said, adding that the bacteria had not been "weaponised" - altered to make it spread more easily in the air.
The 35-year-old postal worker infected by skin anthrax was taking antibiotics in hospital and is expected to recover, a health official said.
The victim is believed to have handled letters to NBC anchorman Tom Brokaw in New York and Senate Majority Leader Tom Daschle in Washington.
A New Jersey female postal worker was earlier also diagnosed with skin anthrax.
A woman working for the New York Post also contracted skin anthrax, the newspaper's publisher said, adding that she was virtually cured.
Along with the newspaper, all three major TV networks in New York City, the Capitol Hill complex in Washington and a tabloid newspaper company in Florida are now all sites of anthrax infection.
Contamination spreads
A letter sent from Miami to an individual in Buenos Aires showed the presence of anthrax spores, Argentine Health Minister Hector Lombardo said, confirming test results.
Earlier in the week, the Kenyan Government said four people had been exposed to anthrax bacteria in a letter posted from the US.
The US is offering $1m for information on who is behind the anthrax attacks, FBI director Robert Mueller said.
The US postal service is sending cards to every home and business - 147 million addresses - telling people how to deal with suspicious post.
Health authorities and emergency services in New York have complained of being swamped by nervous members of the public demanding nasal swabs and doctors were urged not to prescribe the antibiotic Ciprofloxacin - used to treat anthrax - without good medical reason.
The drug's main manufacturer, Bayer, announced it would treble production.
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