The offer was enticing: handsome returns awaited investors willing to provide an infusion of cryptocurrency to Elon Musk, the billionaire CEO of Tesla and founder of SpaceX, in exchange for a profitable venture. It appeared to be too good to be true, and it was.

Investors lost $2 million in six months to fraudsters impersonating Mr. Musk, according to the Federal Trade Commission in a report released on Monday to draw attention to an increase in cryptocurrency scams.

The commission discovered that nearly 7,000 people lost a total of $80 million as a result of various scams targeting investors in Bitcoin and other cryptocurrencies such as Dogecoin, a nebulous marketplace that Mr. Musk has aggressively promoted on Twitter. According to the commission, the average amount they lost was $1,900.

The surge in fraud cases — a nearly 1,000% increase over the same period last year, according to the report — occurred as the prices of Bitcoin and Dogecoin reached all-time highs. According to the commission’s report, “all of this plays right into the hands of scammers.” “They blend into the scene with claims that may appear plausible because cryptocurrency is unfamiliar territory to many people.”

It was unclear how many people had been duped by the impersonators or whether they had received money solicitations. It was also unclear whether they had used a specific cryptocurrency platform. On Monday night, the commission did not immediately respond to a request for additional information.

Mr. Musk’s representatives at Tesla did not immediately respond to a message seeking comment on Monday night. Tesla disclosed in its annual report in February that it had purchased $1.5 billion in Bitcoin as part of an initiative to invest in alternative assets such as digital currencies and gold bullion.

The news, combined with Mr. Musk’s March announcement that Tesla would accept Bitcoin as payment for cars in the United States, pushed the price of Bitcoin up by more than 10%. Mr. Musk then reversed course this month, stating that the company would no longer accept cryptocurrency due to environmental concerns. Mr. Musk has also sent mixed signals about Dogecoin, which was created in 2013 as a cryptocurrency parody and has recently soared in value.

Last week, he polled his 55.1 million Twitter followers on whether Tesla should accept Dogecoin; 78% said yes. He also revealed last week that SpaceX would launch a satellite to the moon in exchange for a payment in Dogecoin next year.

In an interview on Monday night, Joseph A. Grundfest, a law and business professor at Stanford and a former member of the Securities and Exchange Commission, said that the rise in cryptocurrency scams was unsurprising given the price surge. He stated that when confronted with propositions such as those concocted by Mr. Musk impersonators, investors should be more cautious. Mr. Grundfest advised people not to send cryptocurrency to Elon Musk. “He already has far more than he requires.”

In a report released on Monday, the Federal Trade Commission warned that fraudsters had used online dating platforms to lure people into cryptocurrency scams. According to the report, approximately 20% of the money lost through romance schemes since October was sent in cryptocurrency. The commission also found that people between the ages of 20 and 49 were more than five times more likely than older people to report losing money on cryptocurrency investment scams.

Experts in cryptocurrency warned that it was especially difficult for victims of fraud schemes to recover their funds, and that cryptocurrency had become a preferred payment method for those orchestrating ransomware attacks.

“There is no practical recourse,” Mr. Grundfest said. “What is the point of cryptocurrency?” It’s a piece of cake. It’s extremely difficult to track.”