At various points on his Fox News program, the anchor Shepard Smith irritated Rush Limbaugh, teased Glenn Beck and grilled Samuel J. Wurzelbacher (a k a Joe the Plumber) over his attacks on President Obama. But it was not until he forcefully confronted the topic of hateful e-mail  some from Fox’s own viewers  that he drew fire over his approach.

On June 10, Mr. Smith was in the middle of three hours of coverage of the killing at the Holocaust Museum in Washington, in which officials identified an elderly anti-Semite as the killer. He then mentioned a prior warning by the Department of Homeland Security about right-wing extremist groups and connected that to the angry e-mail messages he had been receiving.

“When a crazy man has walked into a Holocaust museum and shot the security guard, maybe that’s an appropriate time to warn people: you’ve got a crazy person in your life, keep an eye on him,” he said in an interview in his Manhattan office last week.

Mr. Smith said he fully anticipated one result of those comments: the nasty e-mail increased.

“Thousands of them,” Mr. Smith said. “And I know they don’t mean the things they say. I know they don’t hate me and want death on my family.”