Legal marijuana merchants like Mr. Kunkel — mainly medical marijuana outlets but also, starting this year, shops that sell recreational marijuana in Colorado and Washington — are grappling with a pressing predicament: Their businesses are conducted almost entirely in cash because it is exceedingly difficult for them to open and maintain bank accounts, and thus accept credit cards.

The problem underscores the patchwork nature of federal and state laws that have evolved fitfully as states have legalized some form of marijuana commerce. Though 20 states and the District of Columbia allow either medical or recreational marijuana use — with more likely to follow suit — the drug remains illegal under federal law. The Controlled Substances Act, enacted in 1970 classifies marijuana as a Schedule I drug, the most dangerous category, which also includes heroin, LSD and ecstasy.

As a result, banks, including state-chartered ones, are reluctant to provide traditional services to marijuana businesses. They fear that federal regulators and law enforcement authorities might punish them, with measures like large fines, for violating prohibitions on money-laundering, among other federal laws and regulations.

“Banking is the most urgent issue facing the legal cannabis industry today,” said Aaron Smith, executive director of the National Cannabis Industry Association in Washington, D.C. Saying legal marijuana sales in the United States could reach $3 billion this year, Mr. Smith added: “So much money floating around outside the banking system is not safe, and it is not in anyone’s interest. Federal law needs to be harmonized with state laws.”