The bill has not yet come before the Board of Supervisors, but is expected to be introduced this fall, according to the mayor's office.
In a prepared statement Newsom said, "The point here is to boost our recycling rate to above 90 percent," up from the current 70-percent rate.
"We don't need outrageous fines to do that," he said.
The $500 to $1,000 fines were "place holder" numbers in a bill drafted by the Department of the Environment, the mayor's office stated.
According to Newsom, the main goal of the proposed law is to have recycling and composting available to tenants in buildings that do not offer those services.
The fines would heighten public awareness and encourage compliance, he said.
Fines over $100 might still apply to businesses and landlords who refuse to offer recycling and composting opportunities to tenants, according to the mayor's office.