The latest numbers show Republican Paul Coble received 359 more votes than Democrat Stephanie Fanjul.
"We're still very optimistically cautious," Coble says. "We feel good about it, and time will tell the story."
Fanjul sat beside Coble at Wednesday's city council meeting, and she is not conceding defeat until all of the numbers are in.
"That's what this is all about, is being sure we get the right number," she says. She says the goal of the counting is to ensure that voters and the winning candidate get the "final, real number."
Election officials will get the final number by hand counting ballots that were cast at the wrong precinct, so-called "provisional ballots," and ballots that did not pass through the electronic counters. There are 278 uncounted provisional ballots.
Members of the Wake Board of Elections say they hope to declare a new Raleigh mayor by 11 a.m. Friday, but they cannot say with certainty that they will be able to do so.
Neither candidate would say whether he or she plans to ask for a recount once the board determines a winner. Candidates can ask for a recount if the difference between them is 1 percent or less.