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Attempts by U.S. citizens at carrying out unsophisticated terrorist attacks in the United States have increased sharply in recent years. The latest example was Faisal Shahzad, who confessed in court this week that he left a vehicle rigged with explosives in New York’s Times Square on the evening of May 1. In court testimony, he also admitted to having trained in bomb making with the Pakistani Taliban.

A recent Rand Corp. study of so-called “homegrown” U.S. radicalism reported a significant increase in indictments of Americans who were recruited for jihadist violence in the past two years.

The report said 81 were indicted for terrorism-related crimes between 2002 and 2008. Forty-two people were indicted for such crimes in 2009, and two more have been indicted in 2010.

The study, authored by former U.S. special-operations officer Brian Jenkins, concluded that one in 30,000 Muslim Americans is vulnerable to radicalization, a fact “suggesting an American Muslim population that remains hostile to jihadist ideology and its exhortations to violence.”

In the interview Thursday, Mr. Brennan also said that the vision of Islam put forth by Osama bin Laden and other al Qaeda leaders was widely rejected by the Muslim world. Last month, Mr. Brennan drew criticism for a speech in which he said, “Jihad is holy struggle, a legitimate tenet of Islam, meaning to purify oneself or one’s community.”

Mr. Brennan said that he opposed granting any legitimacy to what he called al Qaeda’s “twisted” interpretation of Islam.

“Clearly, bin laden and al Qaeda believe they are on this very holy agenda and this jihad,” he said. “However, in my view, what we cannot do is to allow them to think, and the rest of the world to think, and for the future terrorists of the world to believe al Qaeda is a legitimate representation of jihad and Islam.”

Mr. Brennan also said that the U.S. law enforcement community has the means to monitor Web forums affiliated with al Qaeda that have in the past proven to be a gateway for recruitment into the terrorist organization.

But he also said that any investigations or monitoring of such sites needed to first pass a threshold of probable cause.

“There needs to be some type of predicate or premise for there to be reasonable suspicion that someone is engaged in activity that is unlawful,” he said. “The mere engagement in political speech, even if it is radical, is not in itself a cause for investigation.”

Mr. Brennan toward the end of the interview acknowledged that, despite some differences, there is considerable continuity between the counterterrorism policies of President Bush and President Obama.

“There has been a lot of continuity of effort here from the previous administration to this one,” he said. “There are some important distinctions, but sometimes there is too much made of those distinctions. We are building upon some of the good foundational work that has been done.”