The cases are under criminal investigation
"I think the only responsible thing for us to do is proceed on the basis that it could be linked," said Mr Cheney.
He spoke after a woman employed by the NBC television network in New York was found to have become infected with anthrax after opening mail addressed to the station's main news presenter.
It followed the confirmation of three cases - one of them fatal - at media organisations in Florida that have led to the launch of a criminal investigation.
Other cases of suspicious mail, at the State Department in Washington, the New York Times and a subsidiary of the Microsoft Corporation in the state of Nevada, are being investigated.
The cases have heightened the fears of Americans in the wake of the 11 September terror attacks on the country that have been blamed on Bin Laden.
Both the letter that the NBC employee opened and the one to the New York Times were posted from Florida.
Many media companies have refused to accept new mail in the wake of the New York case, and some New Yorkers have been turning up at hospital emergency facilities or buying the antibiotic used to treat anthrax.
New York's Mayor, Rudolph Giuliani, has urged people not to panic. Anthrax was not contagious, he said.
Experts believe the anthrax so far discovered is not the specially-made weaponised type which would be used in an attack of mass destruction.
Correspondents say New Yorkers have so far remained calm, with cafes and theatres full on Friday night.
Training manuals
Mr Cheney told PBS Television: "We know that [Bin Laden] has over the years tried to acquire weapons of mass destruction, both biological and chemical weapons.
"We know that he's trained people in his camps in Afghanistan. For example, we have copies of the manuals that they've actually used to train people with respect to how to deploy and use these kinds of substances.
"So, you start to piece it altogether. Again, we have not
completed the investigation and maybe it's coincidence, but I must
say I'm a sceptic."
The vice president's comments followed an earlier statement by Attorney General John Ashcroft, who said there was no evidence linking the four cases with terrorist actions.
They came after a warning from the Federal Bureau of Investigation (FBI) that there might be more terrorist attacks within the US in the next few days as a response to the US-led bombing of Afghanistan, whose ruling Taleban regime is sheltering Bin Laden.
Media targets
Unease about a potential biological attack by terrorists has mounted since a man died on 5 October after inhaling anthrax, and two others were infected after testing positive for exposure in a separate incident in Florida.
The latest anthrax case in New York - which is also the subject of a criminal investigation - involves a woman who is believed to be an assistant to NBC news anchor Tom Brokaw.
She was in no danger and was responding well to treatment with antiobiotics, the broadcaster said in a statement.
Cutaneous - or skin - anthrax is much less deadly than the respiratory form which caused the infections in Florida.
The three Florida cases were also linked to a media company, American Media Inc.