In a speech to supporters, Meeker said he would request a runoff.
"This is just a great, great crowd, and a great day for Raleigh," Meeker said. "And it's a great day for Raleigh because the better growth message has won tonight."
"Raleigh needs a Mayor who will help our city grow better, not just bigger," he continued. "We need a Mayor who is proactive and will move this city forward."
"The race tonight is very, very close, just a difference of about three votes per precinct," Meeker said. "Subject to the counting of the provisional ballots which will occur on Thursday, I will call for a runoff so we can beat Paul Coble in November."
Coble found himself in a runoff when he ran against Stephanie Fanjul in 1999 for the post he now holds.
Tuesday night's victory party was like dejà vu.
"We have won but, as we are used to, it is a thin margin of victory," Coble said. "Apparently my opponent has called for a runoff and I'm not surprised by that, and we're used to that."
Coble said he will spend the next 30 days campaigning.
"We've got 30 days. We start tomorrow morning, and we're going to finish this thing the way we started it," Coble said. "We're going to do it positively. We're going to talk about the success that we've had and how Raleigh is headed in the right direction, and we're going to keep heading in the right direction, especially with the help I've got with this new council."
Meeker says his supporters want to change direction. Among his supporters are residents of Raleigh's Oberlin neighborhood who were happy to see plans for a big development there fall through.
People may be able to see where the candidates stand on this issue and more if Coble accepts the challenge Meeker said he would issue.
"I'm going to challenge him to a debate with a neutral moderator," Meeker said. "So all the citizens can hear what the issues are and what the next mayor of the city needs to do."
Coble did not say whether he would accept the challenge.
Fewer than 40,000 people -- under 20 percent of the electorate -- voted for one of the mayoral candidates.
Tuesday's results are unofficial. Absentee ballots will be counted Thursday and the elections board will tally the final count Friday. If Coble still has less than a majority of the total votes cast, Meeker can request a November runoff.
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