The committees diluted the proposed ordinance without approving it, but sent the amended measure to the full L.A. City Council.
The City Council is expected to address the proposed ordinance Wednesday morning.
The city's attorney's office wants to ban the sale of marijuana for profit, among other strict regulations being proposed.
The proposed ordinance says medical marijuana collectives would be able to grow pot for members with serious illnesses only. They would be nonprofit collectives, and over-the-counter sales would be banned.
Collectives would only be able to have no more than 5 pounds of dried pot, or 100 plants, at any given time.
There are also restrictions as to where these collectives can be located in the ordinance. For example, they cannot be located near a school, a religious organization or another collective.
Both committees want the council to come up with an ordinance that is both fair and safe.
"We have a city to take care of. We also have individuals who need this medicine. My goal is to make sure we allow for this access, and we do provide protections for our communities," said L.A. City Coucilman Ed Reyes.
The National Organization for the Reform of Marijuana Laws (NORML) says the city could lose between $36 million and $74 million in sales-tax revenue each year.
The Union of Medical Marijuana Patients will sue the city if an ordinance such as this is passed.
"I, like many senior citizens, can't smoke marijuana, but we can eat our medicine, which keeps us able to function," said medical marijuana user James Green.
Reyes said his goal is to have the ordinance before the full city council to vote on within the next couple of weeks.