The U.S. House of Representatives will vote “in the next few weeks” on a bill that would protect banks working with state-legal marijuana companies from federal regulatory penalties, Rep. Jim McGovern said Wednesday.

Though it would not solve all of the issues marijuana businesses face due to conflicting federal and state laws, congressional action that could encourage more banks to serve the growing and newly legal industry would eliminate one headache and could improve public safety around marijuana businesses.

On Boston Herald Radio, the U.S. House Rules Committee chairman said he will clear the way for the cannabis banking bill to reach the House for a vote.

“In the House, we will move on this issue in the next few weeks. It will come to the Rules Committee, which I’m the chairman of, and we will guide it to the House floor for a vote,” the Worcester Democrat said. “I think it will pass with an overwhelming vote, Democrats and a lot of Republicans as well.”

Under the Secure and Fair Enforcement (SAFE) Banking Act, federal banking regulators could not “prohibit, penalize, or otherwise discourage a depository institution from providing financial services to a cannabis-related legitimate business or service provider” and could not terminate or limit deposit insurance.

Because marijuana remains wholly illegal at the federal level, businesses have struggled to find banks, most of which operate under federal regulations and with federal insurance, willing to accept them as customers.

“Especially with regard to the banking issues, everything now is being done in cash. This is not the way we want this to go,” McGovern, a co-sponsor of the SAFE Act, said. “We need to make sure the federal laws respect what the states are doing. So that’s going to happen.”

The bill states its purpose is to “increase public safety by expanding financial services to cannabis-related legitimate businesses and service providers and reducing the amount of cash at such businesses.”

Cannabis Control Commission Chairman Steven Hoffman has highlighted the need for more banking services in the marijuana industry. Three Massachusetts banks were serving marijuana businesses as of a month ago and Hoffman said the CCC was talking with three more about serving the newly legal industry.

“I’m reasonably comfortable that we’re bringing banks in at a pace that is consistent with the pace at which we’re opening,” Hoffman said last month. “The current licensees that are operational, I believe, are all banked … even though I would like to move the banking process along more quickly, obviously there is a limit to what I can do but I’m comfortable that we’re moving at a pretty good clip there.”

McGovern said he does not know the status of a marijuana industry banking bill in the Republican-controlled U.S. Senate – where U.S. Sen. Elizabeth Warren sponsored a similar bill – but he expects a bipartisan House vote in support will put pressure on the Senate to act later this year.

“What we’re finding here is that the states that are moving forward on the issue of marijuana are not just Democratic blue states, but they’re also Republican red states. You have liberal Democrats and you have conservative Republicans and you have everybody in between all understanding that it makes sense to update our laws,” he said.