Spokesman Richard Boucher called the remarks -- which Robertson made last week on his nationally televised "700 Club" program -- "despicable" and a senior department official said a protest had been made "at the highest level."
"I lack sufficient capabilities to express my disdain," Boucher told reporters when asked about Robertson's comments. "I think the very idea, though, is despicable."
The senior official said Robertson had been made aware of Secretary of State Colin Powell's extreme outrage at the tone and content of the remarks.
"That's not the way one expresses an opinion in Washington," the official said, adding that Robertson's conduct had been "outrageous."
Robertson, who has been a frequent critic of the State Department, made the offending comments during an interview with a like-minded critic of US diplomacy, columnist Joel Mowbray, who has written a book entitled "Dangerous Diplomacy: How the State Department Threatens American Security."
"I read your book," Robertson said, according to a transcript of the interview posted on his Christian Broadcasting Network's website (www.cbn.com).
"When you get through, you say, 'If I could just get a nuclear device inside Foggy Bottom, I think that's the answer'," he said.
"I mean, you get through this, and you say, 'We've got to blow that thing up.' I mean, is it as bad as you say?" Robertson asked.
Mowbray responded: "It is."
Mowbray's book accuses the State Department of endangering the security of the United States by allegedly cavorting with sponsors of terrorism, negligence or incompetence in the visa issuance process and ignoring the travails of US citizens abroad.