"He's got two years left on his term. Los Angeles can take one for the team," said Melina Abdullah, co-founder of Black Lives Matter-Los Angeles. "Garcetti ain't going to D.C."
The size of the demonstrations has fluctuated over the week. Organizers said several hundred people attended protests over the weekend.
There have been two arrests for failure to disperse during the week of protests, said Los Angeles Police Department spokesman Josh Rubenstein.
It's unclear if the mayor and his family have been home during the demonstrations.
Black Lives Matter member David Cunningham, 22, said he came out Monday to bring attention to the rising numbers of arrests of homeless people that have occurred under Garcetti.
Cunningham, a law student at the University of California, Los Angeles and grandson of former Los Angeles City Councilman David Cunningham, also pointed to skid row's disproportionate population of Black residents.
He accused Garcetti, who served as City Council president before becoming mayor, of effectively ignoring the downtown neighborhood, where thousands of people live in squalid conditions.
"His policies have negatively affected Black Angelenos," Cunningham said.
Bus Riders Union organizer Martinez said that Garcetti met with his group in 2014. The mayor told the group he was moving toward the goal of free transit, Martinez said.
Instead, the mayor, who serves on the board of the Metropolitan Transportation Authority, backed a hike in monthly bus fares.