The House is set to vote on a series of high-stakes bills backed by the cryptocurrency industry, after top Republicans brokered a deal with a group of dissenters in their ranks.

After days of dysfunction that paralyzed the House, Republicans on Thursday moved toward passing a series of bills backed by the cryptocurrency industry, reviving plans for a widely publicized “crypto week” on Capitol Hill that had collapsed amid G.O.P. infighting.

Late Wednesday night, Republican leaders managed to quell a conservative revolt over the measures and finally win a nearly 10-hour vote to take them up. The breakthrough put the House on track on Thursday to pass the Genius Act, which would outline rules for stablecoins, a type of digital currency. That would then clear the legislation for President Trump, who has promised to sign it.

The House is also slated to vote on a separate bill called the Clarity Act, which would establish a new regulatory framework for cryptocurrencies, weakening the power of the Securities and Exchange Commission, which has aggressively pursued crypto enforcement, to police the industry. A third bill that would ban the federal government from offering its own digital currency was also on track for a vote Thursday afternoon.

The action was a sign of the industry’s increasing clout in Washington. After spending more than $130 million to influence last year’s congressional races, crypto companies now enjoy astonishing access to the Capitol and the White House. Mr. Trump is a vocal supporter, with an expansive array of digital currency ventures that have generated billions of dollars for him and his family.

But for the last couple of days, the so-called crypto week appeared in danger of unraveling.

A group of dissenting Republicans, including Representative Marjorie Taylor Greene of Georgia, blocked the bills from coming up, insisting that they be combined into a single piece of legislation. They wanted to ensure enactment of the ban on so-called central bank digital currencies or C.B.D.C.s — a type of crypto created by the federal government that many in the industry view as a threat to privacy.

They agreed to proceed after securing a commitment from Republican leaders that they would attach the prohibition on a government-backed cryptocurrency to the annual defense policy bill, which lawmakers in both parties consider “must-pass” legislation, thus maximizing the chances that it will be signed into law.

Concerns over C.B.D.C.s are largely theoretical. No U.S. official has ever announced plans to create one. But the defection of top Republicans was enough to throw the crypto industry’s entire legislative agenda into uncertainty, at least briefly.