Joseph Curseen died after inhaling anthrax spores
Across the city the investigation is continuing into the discovery of traces of anthrax in three offices on Capitol Hill.
There are now 11 places in the centre of Washington where the bacterium has been found, and 10,000 postal workers have been put on antibiotics.
In New Jersey a post office was closed on Saturday after signs of anthrax were found there, and more postal employees are likely to join those already on antibiotics.
Postal worker Joseph Curseen died after inhaling anthrax spores at Washington's main Brentwood sorting office.
His was the second such funeral in the city in as many days and his colleagues across the country have come to feel they are in the anthrax front line, says a BBC correspondent in Washington.
In Washington in particular, undelivered mail is piling up.
Unopened mail
Forty-five truck loads are being sent to a specialist plant in Ohio to be decontaminated by equipment normally used for hospital implements.
Letters sent to senators and members of Congress have gone unopened for days.
In the latest scare on Capitol Hill, spores were found in three offices, but the contamination is being treated as low level.
While the search goes on for the person who posted the original anthrax letters, questions remain over whether it is the work of a foreign activist or some domestic extremist.
Handwriting analysts suspect the same person wrote all three letters.
At present the only known source of anthrax in Washington is the letter sent to Senator Tom Daschle.
Investigators say either there are more undiscovered letters or anthrax spores are being spread through the postal system after being picked up by sorting machines.
Other outbreaks
In New York, anthrax has been detected on four mail-sorting machines at a processing station that handles millions of parcels a day.
In an earlier outbreak at a tabloid newspaper in Florida, two men contracted inhalation anthrax, one of whom died.
There have also been cases of cutaneous, or skin anthrax, a less serious form of the disease, in several New York media offices and mail offices in New Jersey.
Seven people are known to have been infected with it.