"In terms of a specific opening date, it's premature to mark that. Our focus with the Market House is not just to get it open, but to get it done well," Cohen said.
The reopening, he said, will begin a "new chapter of the Market House's history."
The 19th-century waterfront building was flooded in 2003 during Tropical Storm Isabel, and since then has faced disputes with renters and political opposition.
City efforts in the past year have focused on renovating the structure and filling it with a mix of vendors.
Cohen said he expects to make tenant announcements no sooner than the second week of January, and vowed that the revived Market House would not be a food court, but would feature a "good mix of offerings and primarily local vendors to draw the locals."
"We'll see," said Ross Arnett III, the Ward 8 alderman who has long been outspoken against the city's continuing efforts to have vendors flourish in its building at City Dock. "My position even four years ago is that the city shouldn't be in the business of running a business."
He predicted that a lot of effort will have gone into ending up with "a food court, not a market."
Rhonda Wardlaw, city spokeswoman, said in an email that the latest round of renovations cost less than $100,000. Upgrades to restrooms and ventilation, and also the addition of seating with a view of the city's harbor, have been part of the renovation plan.
Cohen had vowed to "walk the plank" into Ego Alley — the city harbor — if Market House didn't reopen by Oct. 1, 2012.
Neither happened. The mayor said he'll now step into the cold waters, as a publicity event, when the Market House reopens in the spring.