The proposition was tantalizing: Handsome returns awaited investors who would be willing to provide an infusion of cryptocurrency to Elon Musk, the billionaire chief executive of Tesla and founder of SpaceX, for a moneymaking venture.

It seemed too good to be true, because it was.

Investors lost $2 million in six months to fraudsters who impersonated Musk, the Federal Trade Commission said in a report released Monday that was meant to draw attention to a spike in cryptocurrency scams.

The commission found that nearly 7,000 people lost a reported $80 million overall from October through March as part of various scams targeting investors in Bitcoin and other cryptocurrencies like Dogecoin, a nebulous marketplace that Musk has bullishly promoted on Twitter. The median amount that they lost was $1,900, according to the commission.

The spate of fraud cases — a nearly 1,000% increase compared with the same period the previous year, the report said — came as the price of Bitcoin and Dogecoin soared toward record highs.

“All of this plays right into the hands of scammers,” the commission’s report said. “They blend into the scene with claims that can seem plausible because cryptocurrency is unknown territory for many people.”

A spokeswoman for the commission said in an email Tuesday that officials had received 133 complaints from people claiming to have been duped by the impersonators. They said they had seen videos on YouTube with text running across the screen alerting them to a supposed “giveaway” from Musk, the spokeswoman said.

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Some told the commission they had responded to tweets that they mistakenly thought were from Musk. The giveaway offers promised to immediately multiply the Bitcoin investments that people sent to Musk, the spokeswoman said.

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Representatives for Musk at Tesla also did not immediately respond to a message seeking comment Monday night.

The electric-carmaker disclosed in its annual report in February that it had bought $1.5 billion worth of Bitcoin, which Tesla said was part of an initiative to invest in alternative assets like digital currencies and gold bullion.

The revelation, along with Musk’s announcement in March that Tesla would accept Bitcoin as payment for cars in the United States, sent the price of Bitcoin skyward by more than 10%. But then Musk reversed course this month, saying that the company would no longer accept the cryptocurrency because of concerns over its impact on the environment.

Musk has similarly sent mixed messages regarding Dogecoin, which was created as a cryptocurrency parody in 2013 and has recently been booming.

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Last week, he polled his 55.1 million followers on Twitter on whether Tesla should accept Dogecoin; 78% of respondents said yes. He also revealed last week that SpaceX would launch a satellite to the moon next year in exchange for a payment in Dogecoin. In a May 8 appearance on “Saturday Night Live,” Musk said that cryptocurrency was both “the future of currency” and “a hustle.”

Joseph A. Grundfest, a professor of law and business at Stanford and a former member of the Securities and Exchange Commission, said in an interview Monday night that the surge in scams involving cryptocurrency was not at all surprising amid the surging prices.

He said that investors should be more circumspect when faced with propositions like those concocted by the impersonators of Musk.

“Don’t send cryptocurrency to Elon Musk,” Grundfest said. “He already has more than he needs.”

The FTC cautioned Monday in the report that fraudsters had used online dating platforms to lure people into cryptocurrency scams. About 20% of the money that people reported losing through romance schemes since October was sent in cryptocurrency, the report said.

The commission also noted that people ages 20-49 were more than five times as likely as older people to report losing money on cryptocurrency investment scams.

Cryptocurrency experts cautioned that it was especially difficult for victims of fraud schemes to get their money back and that cryptocurrency had become a preferred payment method for those orchestrating ransomware attacks.

“As a practical matter, there is no recourse,” Grundfest said. “Why crypto? It’s very simple. It’s very hard to trace.”