Spencer Pratt and Nithya Raman are in a slow-speed chase for the chance to advance to the November election for mayor of Los Angeles.

Mr. Pratt, a reality TV star and registered Republican, ended election night on Tuesday with 30.4 percent of the nearly 500,000 ballots tabulated to that point in the primary.

But hundreds of thousands of ballots still remained to be counted over the course of the following few weeks, and those ballots were expected to favor Democrats. That raised the question of whether Ms. Raman, a progressive Democrat who ended election night with 22.3 percent of the vote, could catch up.

In updates to the vote count provided on Wednesday and Thursday, Ms. Raman did notably better among the 60,000 newly counted ballots than Mr. Pratt. On Thursday evening, Mr. Pratt’s share of the vote tabulated so far was down to 29.4 percent, and Ms. Raman’s share was up to 23.4 percent.

Karen Bass, the Democratic incumbent mayor of Los Angeles, remained in first place with 35 percent of the vote and will proceed to the November election.

Los Angeles County wasn’t able to provide an estimate of the number of ballots that remained to be counted in the city. But based on historical patterns and other data, there could be between 250,000 and 300,000 ballots from city voters left to count in the race.

If that estimate is correct and if the shares that Mr. Pratt and Ms. Raman got in Wednesday’s and Thursday’s vote reports are indicative, Ms. Raman could be within range to surpass Mr. Pratt for the No. 2 spot in the race.

But there’s no guarantee that the current trend will remain consistent. Certain portions of the remaining ballots could be substantially better or worse for either candidate if there is significant variation in the geographic or demographic makeup of the voters whose ballots remain to be counted.

For example, utilizing a drop box is the most common way to return a ballot in Los Angeles County, followed by returning one through the mail, according to Mike Sanchez, a spokesman for the office of the registrar-recorder and county clerk. If drop-box voters support Mr. Pratt at different rates than mail voters do, that could make it difficult to assess whether Ms. Raman is on track to overtake him. And while the county generally processes ballots in sequential order, Mr. Sanchez was not able to provide a breakdown of the return method of the votes that had been released so far.

Los Angeles County will report additional ballots every day until at least Friday, June 12. On Wednesday and Thursday, the county reported about 80,000 new ballots countywide, with about 30,000 of those each day being ballots from the city. The county hopes to increase the number of ballots counted each day over the next few days, as more ballots get scanned into the system and are signature verified, according to Mr. Sanchez.

Ballots that were postmarked by Election Day can still be counted as long as they are received by the end of the day on Tuesday, June 9.

Luke Vrotsos contributed reporting.