Mirkarimi received about 38 percent of the first-place votes in the election, compared to about 28 percent for former undersheriff Chris Cunnie and 27 percent for sheriff's Capt. Paul Miyamoto, according to complete unofficial election results.
The candidates are running to become San Francisco's first new sheriff in 32 years, replacing outgoing Sheriff Michael Hennessey, who announced earlier this year that he was not running for re-election.
Cunnie and Miyamoto have touted their law enforcement experience in the race while Mirkarimi, who was elected to the Board of Supervisors in 2004, has the support of Hennessey, an outsider when he began overseeing the department.
David Latterman, a lecturer on politics for University of San Francisco, said Mirkarimi is in good position to become sheriff after Tuesday's first round of the ranked-choice voting process.
San Francisco's system allows voters to rank up to three candidates. If no one reaches a majority, candidates with the lowest first-place vote totals are eliminated and their second- and third-place votes are reassigned until someone gets to at least 50 percent.
"It's going be hard to unseat (Mirkarimi), but it's possible if every other candidate was adamant that no one else should vote for him," Latterman said.
Whoever takes over as sheriff will have to deal with new state legislation that went into effect last month moving certain offenders from state to county jurisdiction.
Under the new realignment law, people convicted in San Francisco of nonviolent, non-serious offenses -- as well as adult parolees and juvenile offenders -- are now being overseen by the county, an estimated additional load of up to 700 offenders.
The city's Department of Elections was expected to release updated results in the race at 4 p.m. today.