But the Los Angeles Times reported that she called Garcetti early Wednesday to concede.
According to Mayorkas and Garcetti, the case against Furrow in federal court will proceed first.
After polls closed on Tuesday, Mr Garcetti reminded his supporters the race was not over.
BBC: Run-off election for Los Angeles mayor after split poll
And it was - there was election of Eric Garcetti, who's a member of the city council.
NPR: With White House Bogged Down By Scandal, GOP Looks For Boost
Councilman Eric Garcetti won 33% of the vote, while Controller Wendy Greuel took 29%, preliminary results showed.
BBC: Run-off election for Los Angeles mayor after split poll
Garcetti's mother is Jewish, and his father, Gil, the former district attorney whose office lost in the O.
"I always felt myself to be Jewish and Latino very comfortably, " Garcetti told the Jewish Journal during the campaign.
In 2001 Gil Garcetti traveled to West Africa for the first of what would be several visits to the continent.
In 2006 his work was exhibited at the Fowler Museum in the exhibition Dance in Cuba: Photographs by Gil Garcetti.
While Garcetti could become the first Jewish man elected mayor, he would not be the first Jew to hold the job.
Greuel's attack ads hit Garcetti for a fundraiser organized by a developer who she says once served prison time for fraud.
Greuel and Garcetti emerged from a March primary in which no candidate secured the majority needed to win outright, leading to Tuesday's runoff.
If elected, Mr Garcetti would become Los Angeles' first Jewish mayor, while Ms Greuel would be the first woman to hold the office.
BBC: Run-off election for Los Angeles mayor after split poll
Eric Garcetti now becomes the first elected Jewish mayor, and also at the age of 42, is the youngest mayor in more than a century.
NPR: With White House Bogged Down By Scandal, GOP Looks For Boost
The preliminary numbers pegged Garcetti at 52 percent and Greuel at 48 percent, with about 6, 100 votes separating them out of about 176, 000 counted so far.
Garcetti's commercials labeled Greuel "DWP's mayor, " a reference to the Department of Water and Power, whose workers financed ads to help install her at City Hall.
Known for his long career as a prosecutor and a Los Angeles District Attorney, Gil Garcetti has spent more than forty years as an urban photographer.
Gil Garcetti est photographe urbain depuis plus de quarante ans.
"Thank you Los Angeles -- the hard work begins but I am honored to lead this city for the next four years, " Garcetti, 42, wrote on Twitter on Wednesday morning.
Garcetti's office already has issued a criminal complaint charging the 37-year-old avowed white supremacist with attempted murder in the same case, attempted murder in the Jewish center case and carjacking.
First of all, a lot of money was spent mostly on - by Greuel and her labor allies, and apparently Garcetti hit that, hit the fact that Greuel was supported by labor unions to his advantage.
NPR: With White House Bogged Down By Scandal, GOP Looks For Boost
On Monday, Greuel sent off a final round of recorded endorsements from former President Bill Clinton, in whose administration she once worked, while Garcetti was on campaign stops arguing a simple point to mostly indifferent residents: The election matters.
The grand jury action in the death of Joseph Santos Ileto, gunned down while delivering the mail eight miles away from the Jewish center, was jointly announced by U.S. Attorney Alejandro Mayorkas and Los Angeles District Attorney Gil Garcetti.
So, anyway, Garcetti will take over...
NPR: With White House Bogged Down By Scandal, GOP Looks For Boost
Eric Garcetti, 42, and Wendy Greuel, 51 - both veterans of city hall - have been cited as mayoral candidates who might face each other in a run-off vote in May if no candidate wins a majority of the vote in Tuesday's election.
BBC: Los Angeles mayoral election under way amid low turnout
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