"We're very confident that the unknowns are behind us at this point," he said.
Because the city is helping to pay for the plaza renovation, City Controller Alan Butkovitz said he might audit the project.
"The repeated delays are causing the costs to rise and raising the possibility of noncompletion," Butkovitz said Tuesday. "We have the authority to conduct an audit, and I am considering doing just that."
Levy said there was no possibility of the project's going unfinished. He said the projected costs for the plaza renovation "are fully covered."
The area remains fenced off to pedestrians and nonconstruction traffic, blocking the west entrance to City Hall. On Tuesday, small excavators were moving around dirt while construction workers drilled and stretched wires along the ground.
The old concrete apron on the west side of City Hall is being made over into a pedestrian-friendly gateway to subway concourses, with a cafe, large lawn, groves of trees, a fountain, and a light display.
Work began in late 2011, and the original cost was set at $50 million. Most of the money is coming from federal and state grants, with $5 million from the city, and substantial contributions from nonprofits, including the William Penn Foundation, and private donors.
By May, the announced cost had risen to $55 million because of the unanticipated underground work. An additional $15 million in SEPTA-related upgrades is being added, including new elevators to the Market-Frankford El and the Subway-Surface Lines, but not to the Broad Street subway station.
Elevators to the Broad Street Line's busiest station must await a long-postponed, $100 million rehabilitation of the City Hall station. Lacking funds, SEPTA has set no date to begin that work.
About 77,000 riders each weekday use the Market-Frankford, Broad Street, and Subway-Surface stations beneath City Hall.
A planned work of public art, Pulse by Janet Echelman, is to feature moving columns of orange, blue, and green mist on the plaza to mimic the movements of the trains on their color-coded lines below.
Inquirer staff writer Claudia Vargas contributed to this article.