Garza held a news conference in the East Side neighborhood after Election Day votes were counted in the 11th precinct. Totals from the precinct weren't available Tuesday night.
Garza won the precinct 275 to 193, giving her an 89 vote lead over Pope.
With all 36 precincts counted, Garza had 5,747 votes, or 50.4 percent, while Pope had 49.6 percent, or 5,658 votes, according to the Chicago Board of Election Commissioners.
"Nobody said it would be easy. But in hearing the voices of people who have been ignored for so long, we together were able to upset the status quo and chart a new path for the forgotten 10th Ward," said Garza in a news release Wednesday.
Meanwhile, Jake Breymaier, Pope's campaign manager, was quick to point out that absentee and provisional ballots have yet to be tabulated. Those votes won't be added until April 23.
"In yet another stunning display of hypocrisy, the Garza campaign is prematurely declaring victory, while themselves acknowledging that all the votes have not yet been counted," Breymaier said in a written statement issued ahead of the challengers' news conference.
"We remain committed to ensuring that all the votes are counted and we remain confident that the alderman will be re-elected." Breymaier said.
On election night, campaign managers for Garza did express concern over absentee ballots. The challenger's staff admitted to placing little focus on absentee ballots for the ward, which includes the neighborhoods of South Chicago, East Side, Hegewisch, The Bush and South Deering.
Pope, a lifelong resident of the Southeast Side, was elected alderman in 1999. He previously served as an assistant to former Mayor Richard M. Daley.
Garza is a Chicago Public Schools counselor at Jane Addams Elementary in the East Side neighborhood. She's also spent her life in the 10th Ward.
Garza was strongly supported by service-sector unions throughout her campaign. In fact, she helped the Chicago Teachers Union organize its 2012 strike. On March 18, the SEIU Illinois Council PAC Fund gave Garza’s campaign a $52,600 injection of cash.
On election night, many of Garza's supporters were seen on the dance floor wearing CTU's signature red T-shirts and sweatshirts — the unofficial uniform of the 2012 teacher's strike.
"There are so many good things that came from the 10th Ward contest," said Garza Tuesday night.
Final election results will be announced after provisional and absentee ballots are tabulated, by April 23.
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