Authorities in the US are stepping up precautions
Concerns have been mounting following confirmation that two postal workers from a Washington facility died of the disease, and news that a female postal worker at a New Jersey office is seriously ill with suspected inhalation anthrax.
The bill is expected to quickly pass through the Senate and be signed into law by President George Bush on Friday.
"This landmark legislation will provide law enforcement and intelligence agencies with additional tools that are needed to address the threat of terrorism," said Representative James Sesenbrenner.
Discount Cipro
Meanwhile, the German pharmaceutical company Bayer Corp has agreed to supply the US Government with up to 300 million tablets of the anti-anthrax drug Cipro.
Cipro is the antibiotic being used to protect thousands of postal workers against the disease and the new deal means a much larger supply will be available.
Bayer agreed to sell an initial batch of 100 million pills to the US Government at a discount price of 95 cents each.
In New Jersey, the female post handler suspected of having inhalation anthrax worked at the mail centre through which anthrax-laced letters addressed to NBC News anchor Tom Brokaw and Senate Majority Leader Tom Daschle passed.
The cases have indicated that letters containing anthrax do not have to be opened to cause a serious threat.
"We're asking people to handle their mail very carefully," Postmaster General John Potter told ABC television. "There are no guarantees that mail is safe."
He also said there was a possibility that a letter which shared a bin with a contaminated letter could itself pick up traces of the bacteria. He stressed however that there had been very few incidents of anthrax in the mail.
Postal workers are angry that Congressional staff were tested immediately after an anthrax-contaminated letter was sent to Mr Daschle last week, but those who had sorted the mail were not tested until five days later.
US Surgeon General David Satcher contended that the public health system was being asked to deal with an issue of which it had virtually no experience.
"The assumption had been that unless letters were opened people could not be contaminated. We were wrong," he said. "This is all new to us."
In New York City, postal workers at five Manhattan facilities are being given Cipro in a bid to counter growing fears of anthrax contamination.
Improved security
In a bid to soothe fear and anger, the postal service has announced it will spend $1bn on new security measures, including machines that use radiation to kill bacteria and spores of diseases like anthrax.
On Tuesday, President Bush also authorised immediate spending of $175m to improve safety at postal facilities.
The postal service is also sending cards to 147 million addresses in America, telling people how to deal with suspect post.
A "Suspicious Mail Alert" poster and a video is being distributed to thousands of mail rooms - both within the postal service and at US businesses, to increase vigilance among workers.
Postal service spokesman Greg Frey emphasised that the first line of defence remained the vigilance of employees.
"We need their watchful eyes and common sense to help us through this period," he said.
Postmaster General Potter has also promised further sweeping measures to prevent the service being exploited by terrorists.
He said that the $1m reward for information leading to the capture of those suspected of carrying out the anthrax attacks still stood.