WASHINGTON — Consumer frauds often make claims that are too good to be true. But a recent one, cited by regulators around the world Wednesday, depended on a pitch that many people found completely believable — that Microsoft or another computer company knows what is on your personal computer.

The Federal Trade Commission announced a multinational crackdown on so-called tech support scams, in which a caller fools a consumer into believing Microsoft or a computer security company has discovered that a PC is infected with harmful software. The caller then offers to fix the computer on the spot for a price. The target would sometimes let the ostensible tech support company gain remote access to his computer, allowing the company to download software to it.

In six cases filed in federal district court in Manhattan, the commission named 17 individuals and 14 companies, most in India, as participants in the operations, including many with legitimate-sounding names like Virtual PC Solutions and Zeal IT Solutions.

At the commission’s request, a federal district judge in Manhattan froze the United States assets of the suspects. The commission also said it had shut down 80 Internet domain names and 130 phone numbers in the United States used in the scheme. Efforts to reach several of the companies and individuals were unsuccessful.