WASHINGTON—Leaders of a Senate committee are set to propose legislation that would assign oversight of the two largest cryptocurrencies, bitcoin and ether, to the federal agency that regulates milk futures and interest-rate swaps.

Senate Agriculture Committee Chairwoman Debbie Stabenow (D., Mich.) and top-ranking Republican John Boozman of Arkansas, are planning to introduce a bill Wednesday that would empower the Commodity Futures Trading Commission to regulate spot markets for digital commodities, a newly created asset class. Currently the CFTC has authority to police derivatives, such as futures and swaps, rather than underlying commodities.

The bill marks the latest salvo in an intensifying battle among federal agencies and congressional committees that oversee them over who will regulate crypto. Thirteen years after bitcoin was created, cryptocurrencies remain largely unregulated by the federal government, leaving investors without key protections from fraud and market manipulation.