Spencer Pratt conceded the Los Angeles mayoral race Friday in a fiery social media video, vowing to continue targeting the city’s political establishment and claiming to possess a recording of one of the two remaining candidates that he says would force her to resign.

Mr. Pratt, a Republican and former star of “The Hills,” finished third in the June 2 primary behind incumbent Democratic Mayor Karen Bass and city Councilwoman Nithya Raman, who will face each other in the November general election. His strong election-night showing — which initially suggested he would advance to the runoff — was reversed over the following week as mail-in ballots were counted. Ms. Raman now holds a lead of roughly 30,000 votes over Mr. Pratt, a margin of about 3.5 percentage points.

“You think you can get rid of me that easily?” Mr. Pratt said in the video, captioned “Saving LA — Phase III” and posted to his social media accounts. “I didn’t get in this for political power. I got in to expose this corrupt machine, and nothing has changed.”

Mr. Pratt said that, no longer constrained by his candidacy, he would be free to speak without having to “worry about offending CNN viewers” or a “campaign hamstringing me now.”

He then issued what he framed as a warning to both Ms. Bass and Ms. Raman, claiming his team has a recording of one of the candidates “doing or saying something that would make her resign in shame.” He said he had been holding the footage for the general election and would release it after the city certifies its November choice. He did not identify which candidate the recording allegedly involves.

“Go ahead and pick your demon, certify your choice, and then you get to see it,” Mr. Pratt said.

Mr. Pratt also predicted an accelerating decline for the city under either candidate, warning that businesses and developers were already planning to leave Los Angeles.

“You have no idea how many major developers, hoteliers, business owners, entrepreneurs have been texting me saying they’re packing up and leaving town,” he said, adding that the departure would reduce tax revenue and force cuts to city services. “You have no idea how bad things are about to get for this city.”

The video concluded with a clip from the television drama “Ozark,” with Mr. Pratt implying that anyone trying to silence him would have to “f——— kill me.”