During an interview Sunday with CBS News Face the Nation Anchor Bob Schieffer, Holder said, "We have to ask ourselves whether the groups that are espousing hate and have their disciples go out and do the kinds of things as in Los Angeles, whether we should be monitoring them more closely."
The Justice Department is limited on what it can and cannot do in tracking hate groups, based on First Amendment rights.
"We can only look at these groups if there's reasonable evidence that they're involved in criminal activity," Holder said. "I think we have to look at the way we apply the regulation, given the new situations we confront."
More and more crimes are being reported as "hate crimes." And Holder said he believes that reflects an actual increase in such offenses.
When asked if his boss, Attorney General Janet Reno, will make a big push for more licensing hand guns in the fall, Holder responded that Reno will follow the president's lead right now.
"The president has spoken in favor of this, but indicated politically it's not something we can do right now, that we need to concentrate on the legislation presently before the Senate, and trying to get reasonable gun regulations passed right now" said Holder.
In claiming that the American people favor stronger gun control legislation, Holder pointed to public opinion polls.
"If Congress will listen to the polls and the American people--every poll indicates the people support these regulations, and I think we have a good chance of ultimately getting it passed."
When asked if he thought that stronger gun control laws might have prevented the Los Angeles shooting, Holder responded:
"It's difficult to say [if] any one incident could be prevented by the passage of a particular statute. If we focus on all the other things that the administration is trying to push, we could certainly reduce the likelihood."