Miller was brought up in New York
Miller, 85 - author of classics such as Death of a Salesman and The Crucible and widely considered the foremost US dramatist of the past half century - comes from New York.
He made his statement about Tuesday's air attacks on the World Trade Center and the Pentagon while in Paris on Thursday.
The Pulitzer Prize-winning Miller said: "Ever since Stalin and the Nazis, reality has transcended fiction."
"There are people who are so enraged by life that they want to kill," Miller continued.
Miller's work is credited for its outspoken nature and for representing the conscience of the 20th Century.
Much of it is also characterised by its expression of tolerance, published at times when it was considered dangerous to voice such views.
Actor
Without going into specifics, Miller told reporters on Thursday that he expected a difficult time ahead for his country in the wake of the attacks.
But he added that he had his doubts about the ability of US President Bush in such testing circumstances.
"He is not a very good actor, he's too obvious most of the time, he has no confidence in his own facade, so he's constantly over-emphasising his sincerity," said Miller.
"He doesn't make for good acting, he doesn't make us easy, he doesn't make us feel comfortable the way a good actor does."
Miller is one of a number of respected figures from the fields of arts and entertainment to speak publicly about the terrorist attacks.
Another is British film director Mike Figgis. The film-maker spoke to BBC entertainment correspondent Tom Brook.
He said this week's events would permanently change the way Hollywood chose to depict violence in its movies.