WASHINGTON—The cryptocurrency industry sought unsuccessfully to limit a provision in the bipartisan infrastructure bill seeking to toughen tax enforcement of crypto transactions. It is now hoping for another shot when the bill moves to the House.

The provision in the roughly $1 trillion plan, approved by the Senate Tuesday, requires brokers of digital assets to report on gains from trading to the Internal Revenue Service. As crafted, it would raise an estimated $28 billion over a decade to help pay for improved roads, bridges, ports and other infrastructure.

Proponents of the Senate’s provision say it would help crack down on tax evasion while also making it easier for crypto investors to meet their tax obligations. Sen. Rob Portman (R., Ohio) was the lead writer of the provision, in consultation with the Biden administration.

But the cryptocurrency industry says the provision was written too broadly and might extend to entities that aren’t brokers and don’t hold customer information. That could inadvertently damp innovation, the industry says.

“Washington politics prevailed over common sense,” said Kristin Smith, executive director of the Blockchain Association, an industry lobbying group, adding this week’s “setback isn’t the end.”

The amount raised by the provision, while relatively small, signals the latest move by Washington policy makers to impose oversight on a $2 trillion industry that has grown dramatically with little regulation. Citing widespread “fraud, scams and abuse,” Gary Gensler, chairman of the Securities and Exchange Commission, last week signaled more-active policing of crypto trading and lending platforms.

Senate Democrats’ $3.5 trillion jobs and infrastructure plan is a sprawling piece of legislation. WSJ's Gerald F. Seib gives a rundown of the handful of provisions that figure to be the most popular, and the ones seen as most controversial. Photo illustration: Todd Johnson The Wall Street Journal Interactive Edition

The Blockchain Association and other groups pushed hard against the provision. A social-media ad released by the association said the provision “is threatening to drive the potential benefits and uses of crypto networks overseas,” and, if implemented, “will affect the future of the internet.”

The video called the measure “generally unworkable” and urged lawmakers to strike it from the bill.

Administration officials worried that narrowing the language of the provision would encourage more industry participants to argue that they aren’t acting as brokers and therefore aren’t subject to reporting requirements.

On Monday, a bipartisan group of Senators announced they had crafted an amendment to clarify that the provision’s reporting requirements don’t extend to software developers and miners that run software to verify transactions for bitcoin and other digital assets.

Sen. Portman and the Biden administration backed the amendment, which appeared to be headed for approval Monday. But a vote was blocked by Sen. Richard Shelby of Alabama, the top Republican on the Senate Appropriations Committee, who had been pressing to secure a vote on his own amendment to provide $50 million to modernize defense infrastructure.

“ ‘I do think there’s enough concern that if we don’t get a fix now, we can fix it at a later time.’ ”

— Sen. Bill Cassidy (R., La.)

Mr. Shelby said Tuesday that he supported the cryptocurrency amendment but wanted to see a vote on boosting military spending. His amendment was also blocked from a vote.

“That’s important—not to overregulate the market,” he said of the cryptocurrency measure, “but our amendment to build the defense infrastructure is more important than anything.”

Lawmakers and industry officials said they planned to continue pressing to modify the cryptocurrency provision.

“I do think there’s enough concern that if we don’t get a fix now, we can fix it at a later time,” said Sen. Bill Cassidy (R., La.), a member of the bipartisan group of 10 senators that crafted the infrastructure bill. “I’d like to see a change.”

The infrastructure bill moves next to the House, where Democratic leaders will be reviewing its final language, according to a leadership aide. However, House Speaker Nancy Pelosi (D., Calif.) has said she won’t bring it to the floor until the Senate passes a sweeping $3.5 trillion budget package that won’t be ready for weeks. Another possibility is that the change is made on a separate piece of legislation, another aide said.

Ms. Smith said the industry hopes to convince House lawmakers to narrow the types of entities that could be considered brokers under the law. If House members don’t change the bill’s language, the industry would try to convince the Treasury Department and IRS to impose those limits when they write regulations to implement the law, she said.

Sen. Mark Warner (D., Va.) said Tuesday that he was talking to Sen. Pat Toomey (R., Pa.), both of whom helped craft the compromise amendment, and others to figure out their next steps.

Sen. Mark Warner (D., Va.) helped craft the compromise amendment.

Photo: Rod Lamkey - Cnp/Zuma Press

Washington policy makers are beginning to more closely scrutinize an expanded cryptocurrency universe that is pushing into Wall Street activities without the investor and consumer protections that apply to traditional securities and financial services.

While securities brokers such as Charles Schwab Corp. and TD Ameritrade long have been required to report clients’ proceeds from stock and other transactions to the IRS, the Treasury Department has yet to require similar reporting from crypto exchanges. Coinbase Global Inc., for instance, tells its U.S. customers to review each of their crypto transactions and calculate gains and losses themselves.

The Treasury already has the legal authority to require crypto exchanges to report information to the IRS and was planning to roll out such requirements in coming years. Rather than granting Treasury new authority, the crypto provision in the infrastructure bill would allow the projected revenue from heightened crypto tax compliance to help pay for increased infrastructure spending.

Separately, a panel of top regulators met last month to discuss stablecoins—digital currencies pegged to national currencies such as the U.S. dollar—that have exploded over the past year as cryptocurrency trading has taken off. A key source of liquidity for cryptocurrency exchanges, the three largest stablecoins—tether, USD Coin and Binance USD—are about $100 billion in value, up from about $11 billion a year ago.

—Dave Michaels contributed to this article.

Write to Andrew Ackerman at andrew.ackerman@wsj.com and Kristina Peterson at kristina.peterson@wsj.com