The Florida outbreak is under criminal investigation
President Bush said the case was a cause for concern but said the government was "responding rapidly".
One man died on 5 October after inhaling anthrax and two others were infected after testing positive for exposure in a separate incident in Florida, sparking fears of an act of bio-terrorism.
The FBI has not established evidence of a link between either case and the 11 September terror attacks in Washington or New York.
But US Attorney General John Ashcroft said that a criminal investigation had been opened into the second case.
Tests are also being carried out on a letter said to contain a mysterious powder which was received by the New York Times on Friday.
Mr Giuliani said some of the building which houses NBC's offices would be closed for a few days for environmental testing and all employees tested for infection.
An NBC statement said that its employee, a woman, was tested positive for cutaneous - or skin - anthrax, which is unrelated to the respiratory form which caused the infections in Florida.
The employee, who is understood to have opened an envelope containing a powder, was in no danger and was responding well to treatment, the statement added.
'Hijack link'
Reuters news agency quoted the editorial director of American Media Inc., in whose offices the Florida infections occurred (AMI), Steve Coz as saying photo editor Robert Stevens may have died after handling a letter contaminated with anthrax spores.
Mr Coz said the FBI was visiting local pharmacies to see if Atta had bought antibiotics used to treat anthrax.
"We know that [Atta] showed up at a pharmacy with red hands. There are people in this area who have a vague recollection of seeing him," he was quoted as saying.
John Ashcroft said on Thursday that authorities suspected foul play.
A third employee, a 35-year-old female worker who has not been identified, also tested positive for the disease.
'Incredible coincidences'
But Mr Coz said the circumstances of the outbreak left little doubt.
Mr Coz said Stevens may have inhaled anthrax without even opening the letter. He would not comment on the letter's contents.
Mr Ashcroft said that US authorities had now investigated about 30 or more potential anthrax scares around the country, but that all the rest were all false alarms.
For the second time this week, there was a security alert at the State Department in Washington on Friday.
The daily televised news briefing was interrupted following the discovery of suspicous white powder in the mail room and the area was sealed off. But FBI investigators have determined the substance was not hazardous.