Jeff Bezos, the founder of Amazon and the owner of The Washington Post, did not become the world’s richest man by refusing to do what it takes to win. And now that he finds himself in a mud fight with the supermarket tabloid that exposed his extramarital affair, he is showing off the same drive that helped him turn a simple idea — selling books on the internet — into an all-purpose, $780 billion powerhouse.

Mr. Bezos has risked significant personal embarrassment in taking on American Media Inc., the company that owns The National Enquirer, which last month devoted 11 pages to the tale of his extramarital affair. But with a personal fortune of more than $130 billion, he has the means to torment his tormentors. And as he showed Thursday with his surprise blog post, which accused the tabloid publisher of “extortion and blackmail,” Mr. Bezos is willing to get dirty in the pursuit of victory.

He has attacked American Media right where it hurts — its shaky legal position — and the strategy is showing early signs of paying off.

Federal prosecutors are reviewing Mr. Bezos’ claim that he has been extorted, according to two people briefed on the matter who were not authorized to discuss it publicly. And those prosecutors have planned a meeting with Mr. Bezos’ representatives, one of those people said.