City Councilman Garcetti launched the People's Pledge on Thursday, a challenge to City Controller Wendy Greuel, City Councilwoman Jan Perry, and attorney Kevin James.
The pledge asks candidates to donate 50 percent of the money used on their behalf by outside groups.
The funds would be donated to charity.
Garcetti, who says he wants to lessen the influence of SuperPacs and independent expenditure committees, first announced the pledge Wednesday night at a mayoral debate in Sherman Oaks.
During the debate, Greuel said she would look at Garcetti's pledge.
On Thursday, her campaign consultant John Shallman said Greuel wouldn't be signing it.
"It's not a people's pledge, it's an Eric Garcetti is afraid of Wendy Greuel pledge," said Shallman.
He accused Garcetti of launching the pledge in reaction to the Los Angeles Police Protective League's recent endorsement of Greuel.
The league represents thousands of police officers, and spends heavily during elections.
"She got a game-changing endorsement," Shallman said. "This is an attempt by Eric to slow down Wendy's momentum."
Perry supports campaign financing reform, said her spokesman Eric Hacopian. But she won't be signing the pledge because she needs matching funds--provided by the city--to compete, he said.
Likewise, James won't stand with Garcetti, said his spokesman. A SuperPAC was launched last year for the Republican candidate.
"Kevin James has made one pledge in this race - a commitment to honest leadership," said spokesman Jeff Corless. "As Mayor, he pledges to ensure Angelenos are finally told the truth about the problems at city hall so that we can fix them once and for all."
Independent expenditure committees and SuperPACs aren't governed by contribution limits and can spend heavily on candidates.
The committees are forbidden from coordinating with the candidates campaigns, but they hold huge influence since they buy advertising, mailers and radio spots.
Garcetti said Wednesday his proposal is modeled after a race in Massachusetts. Last year, Sen. Scott Brown and his Democratic rival, Elizabeth Warren opted to keep SuperPACs out of their race.
His pledge comes the same week a political consultant said the powerful Department of Water and Power union IBEW, which is promising to spend money on an extensive television campaign for Greuel. Two days later, she received the LAPPL endorsement.
A comment from Garcetti's campaign on Thursday afternoon wasn't immediately available.