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Nothing on “Breaking Bad” is quite what it seems: a mild-mannered chemistry teacher is a powerful drug lord; a run-of-the-mill car wash is a sophisticated money-laundering operation. And a darkly comic proposal of mortal violence has led, at least, to offers of a relaxing tropical vacation for the creators and stars of this AMC drama.

On Thursday, the Belize Tourism Board said that it would offer free vacations to Vince Gilligan, the “Breaking Bad” creator and show runner, and eight of its stars, including Bryan Cranston and Aaron Paul, following an offhand and not entirely flattering reference to that Central American nation on Sunday’s broadcast of the show.

In that episode, Saul Goodman, the unsavory lawyer played by Bob Odenkirk, asks the meth-cooking kingpin Walter White (Mr. Cranston) if he has considered sending the nosy D.E.A. agent Hank Schrader (Dean Norris) “on a trip to Belize.” Goodman gingerly reminds White of a former colleague already said to have relocated there – White in fact murdered this person – and an incensed White replies, “I’ll send you to Belize.”

The scene was widely noted on social media, with many commenters wondering if “Breaking Bad” had just turned off audience members who might have been contemplating a (legitimate) trip to Belize.

“Some people may have perceived that to be somewhat of a crisis,” Alyssa Carnegie, the director of marketing and industry relations for the Belize Tourism Board, said in a telephone interview, “but we really thought of it as an opportunity.”

Following Sunday’s episode, the Belize Tourism Board used its Twitter account to post humorous invitations to the “Breaking Bad” actors and characters, asking them to check out the country.

Now it has extended offers to Mr. Gilligan and his cast for each of them to enjoy a four-day, three-night stay in Belize, including airfare, hotel, meals and other activities.

“Many of us are big fans of the show and can’t wait to see what happens over the last six episodes,” the tourism board wrote in its invitation. “While we hope that some of our favorite characters don’t get ‘sent on a trip to Belize’ in the show, we do hope you will take us up on the following offer – we’d like to send all of you on an ACTUAL trip to our country after the season is over.”

Speaking from Belize City, Ms. Carnegie said that her country drew about 1 million tourists annually, often competing with Mexico and Costa Rica for potential vacationers. (Belize, however, does not follow Walter White’s cutthroat strategies for dealing with rivals.)

“We’re a small tourism destination and our competitors are pretty large,” Ms. Carnegie said. “They have huge tourism dollars, so our challenge with that is really trying to make sure that we move a lot with very little. We saw this as a great opportunity to spin the story and introduce a new audience to Belize as a potential vacation destination.”

In addition to Mr. Gilligan, Mr. Cranston, Mr. Paul, Mr. Norris and Mr. Odenkirk, the other “Breaking Bad” stars offered the vacations are Anna Gunn, Betsy Brandt, R. J. Mitte and Jonathan Banks, whose character was sent on the metaphorical “trip to Belize” last year.

Click here to see the invitation from the Belize Tourism Board to the stars of “Breaking Bad” in its entirety.