Representative Nancy Mace of South Carolina, who is spear-heading the legislative effort, described the bill as a "compromise" with less onerous regulations than measures proposed earlier by other lawmakers including Democrats.
The legislation's path in the Democratic-controlled House was uncertain. Mace, a first-term lawmaker, said the measure has five Republican co-sponsors.
Adult use of cannabis is legal in 18 U.S. states and allowed medically in 36 states. But it remains illegal under federal law, which has deterred banks and other investors from involvement with companies that sell marijuana or related products.
"This bill would also support businesses, in particular small businesses. That's very important," Mace told a news conference. "If we were to pass this bill today ... businesses would operate and be legal and regulated just like alcohol."
Titled the States Reform Act, the Republican legislation would defer to state authorities on matters of prohibition and regulation.
It would prohibit marijuana use by those under 21, restrict advertising, protect access to hiring and benefits for veterans who have used cannabis and expunge the records of people convicted on nonviolent, cannabis-only related offenses.
The bill diverges in several important ways from draft legislation proposed in July by Senate Democrats including Senate Majority Leader Chuck Schumer.
Mace's bill would impose a 3% excise tax on cannabis, compared to an increasing Senate tax proposal that would top out at around 25%.
Where the Senate proposal would give the Food and Drug Administration a primary oversight role, the Republican legislation limits FDA involvement to medical marijuana and makes the Treasury's Alcohol and Tobacco Tax and Trade Bureau the primary regulator for interstate commerce.