The U.S. House of Representatives passed a bill Wednesday that would grant legal marijuana businesses access to banking, a measure that would clear up a longstanding headache for the industry.

The bill, called the SAFE Banking Act, passed 321-103 on the strength of near-unanimous support from Democrats and nearly half of Republicans. Its prospects in the Senate are uncertain, but supporters said the amount of Republican support in the House was a good sign.

"This is a sign the time has come for comprehensive cannabis reform," said Morgan Fox, a spokesman for the National Cannabis Industry Association. "The fact that we got almost half the Republicans is a huge sign we're moving in the right direction toward sensible policies."

Thirty-three states have legalized cannabis for medical or recreational use. But the federal prohibition on the drug has made it difficult for businesses in the multibillion-dollar industry to get bank accounts, loans and other financial services.

The bill would allow businesses legitimately operating under state laws to access loans, lines of credit and other banking services, while sheltering financial institutions from prosecution for handling marijuana-linked money.