The Senate Banking Committee approved a bill that aims to give cannabis businesses access to traditional financial institutions in a bipartisan vote Wednesday, teeing up a vote of the full Senate and signaling softening opposition to cannabis reform among some Republicans.

In a 14-to-9 vote, the committee approved the bill, known as the Secure and Fair Enforcement Regulation or “Safer Act,” alongside a handful of amendments.

Senator Schumer said that he would continue to support the bill in the Senate and that he would also be working to advance measures to “expunge records for cannabis offenses.”

The political director of the National Organization for the Reform of Marijuana Laws, Morgan Fox, said that the bill passed was an “improved version” of the Safe Banking Act, which was pulled for revision earlier this year.

“It allows state-licensed cannabis businesses to more easily access financial services, such as opening a simple bank account, and it provides entrepreneurs with greater access to lending and other services that are available to other legal businesses,” Ms. Fox said.

Clearing the way for cannabis businesses to access financial institutions has long been a goal of many in the business, with the need to do business in cash burdensome and often dangerous for retailers and others involved in the industry.

A national cannabis policy lobbying group, the National Cannabis Roundtable, a group where a former House speaker, John Boehner, now acts as an honorary co-chairman alongside the former Secretary of Health and Human Services, Kathleen Sebelius, called the vote “historic.”

“We are heartened to see broad bipartisan support move this bill out of committee,” the group’s director, Saphria Galoob, said in a statement. “We look forward to momentum and support continuing to build as it now moves to the Senate Floor and ultimately the House.”

While the prospects in the full Senate are likely good for the bill, given its bipartisan support in committee, the bill’s chances of passing the House are less clear.

In total, the House has passed similar bills seven times. However, the House has never passed the bill under Republican leadership. While the House is currently grappling with the issue of a looming government shutdown, the bill may face skepticism in committee when it comes time for the House to consider it.

The chairman of the House Financial Services Committee, Patrick McHenry, has been historically skeptical of allowing legal cannabis businesses to bank, citing concerns with the “resulting regulator regime” and potential public health concerns.

The main expected point of contention in the bill, however, has little to do with banking for cannabis businesses. House lawmakers are expected to take issue with Section Ten of the law, which relates to a bank’s power to choose to do business with specific businesses based on the impact on its reputation.

Congressman Blaine Luetkemeyer, who is from Missouri, a state that recently legalized recreational cannabis, told Politico that the bill was “dead on arrival in the House” but not because of Republican opposition to cannabis decriminalization. Rather, he was concerned with how the provision might affect oil, firearm, and cryptocurrency businesses.

The movement in the Senate was still hailed by those in the industry as a major victory for legal cannabis businesses. The chief executive of a group of certified medical cannabis doctors, DocMJ, Aaron Bloom, said it was a signal of “progress and modernization.”

“The medical cannabis sector, long hampered by financial hurdles and regulatory ambiguities,” Mr. Bloom said in a statement. “The Safer Banking Act sweeps away these impediments, offering these enterprises the same financial services and protections enjoyed by any other legitimate business.”