Feuer's demand comes as the city and county are both looking at implementing vaccine mandates. The city attorney also wants the federal government to restrict air travel unless passengers can prove they've been vaccinated or provide a negative COVID-19 test.
He also called for a requirement for public employees to be fully vaccinated or face possible suspension or termination.
City Councilmember Kevin De Leon supports a mandate and believes it will encourage the unvaccinated to get the shot.
"We cannot afford another shutdown of our economy due to a small group of individuals that for ideological reasons, for civil, libertarian reasons refuse to get vaccinated," De Leon said. "Who wants to go to work and be next to an individual who has been unvaccinated?"
Fauci warns 'things are going to get worse' with COVID
Los Angeles officials are hashing out the details of a possible policy that would require all city employees to show proof of COVID-19 vaccinations or weekly negative COVID-19 tests.
Last week, City Council President Nury Martinez and Councilman Mitch O'Farrell introduced a motion requiring proof of at least partial vaccination to enter public indoor spaces in the city. The city council is scheduled to discuss the issue Wednesday.
Meanwhile, the County Board of Supervisors approved a plan to draft a measure that would require proof of vaccination at certain indoor venues.
A growing number of local restaurant owners have taken the matter into their own hands and are requiring proof of vaccination for entry.
At Enzo's Pizzeria in Westwood, owner Lenny Montana wants proof of vaccination for entry, but isn't sure how to enforce it. Montana believes a rule requiring vaccination will protect his staff and make customers feel at ease while eating.
City News Service contributed to this report.