LOS ANGELES (CNS) — He hasn't conceded defeat, but Los Angeles City Councilman Gil Cedillo appeared Friday to officially run out of hope in his effort to retain his District 1 seat, with challenger Eunisses Hernandez again expanding her lead with the release of the latest election results.

According to figures released by the county Registrar-Recorder/County Clerk's Office, Hernandez's lead over Cedillo from the June 7 election grew by 13 more votes to reach 2,402. It was a minor increase, but with only about 7,000 ballots remaining to be tallied from across Los Angeles County — and with only a fraction of them likely to be from council District 1 — Cedillo's re-election bid appears all but over.

The latest tally gave Hernandez, a community activist and public policy advocate, 16,080 votes, or 54.04%, while Cedillo had 13,678, or 45.96%.

On her Twitter page, Hernandez again proclaimed victory in the race.

"Now the hard work begins," Hernandez wrote. "We must stay rooted in not leaving people behind and uplifting and taking the lead of directly impacted people. We will continue to lead our work with love, compassion, deep strategic analysis and patience."

Cedillo has not conceded the race. But fellow Councilman Marqueece Harris-Dawson on Friday acknowledged the inevitable, taking to Twitter to praise Cedillo's accomplishments in elected office and wish Hernandez luck.

"Hopefully history repeats itself and Eunisses is as successful as Gil," Harris-Dawson wrote. "Viva Gil! Viva Eunisses and long live justice in LA!"

In the race for city attorney, civil rights attorney Faisal Gill continued to lead the seven-candidate field with 137,382 votes, or 24.22%. In the race for second place — and a trip to the November runoff election — financial law attorney Hydee Feldstein Soto was holding a razor-thin 178-vote lead over former federal prosecutor Marina Torres.

The next vote-counting update is set to be released Tuesday. According to the Registrar-Recorder's Office, roughly 7,075 ballots countywide still need to be tallied. The results are expected to be completed and certified by July 1.