With 98 percent of precincts reporting, Ald. Willie Cochran had 53 percent of the votes to Smith's 46 percent.
Smith and his attorneys met with election officials Tuesday night, questioning them about the results.
"We want to ensure that it's fair and that every vote is counted, and that people who didn't live in the ward of vacant lots weren't people who were voting. We want to make sure that the 20th Ward voices are heard," Smith said.
"This election is not final tonight, and that's the truth," said Fred Bates, Smith's attorney. "I don't know whether Alderman Cochran has declared victory or not, but we make no concessions."
"We concede nothing," Smith said.
Smith says he wants to see additional voter data before challenging the results in court.Alderman Cochran responded the fraud allegations during a visit to ABC7 Wednesday morning.
"The judges of the election, poll watchers, people at the Board of Elections, none of them are conspiring to create some kind of fake win. This was won in the field, in the battlefield. It was won by voters going into the booth doing what they they do, and that is 53 percent for Willie Cochran," he said.
"The data that will be produced by the Board of Election is open. There is administrative law and procedure that we will be following to review the outcome of this election," said Cochran. "In the end, it'll still be the same results."