"I'm really confident," Denis Oswald said Tuesday. "If this pace is kept up, everything will be ready on time."
The International Olympic Committee has told Olympic organizers that work on the steel-and-glass roof must wrap up by the end of June to allow time to install wiring, technical systems and other upgrades for the Aug. 13-29 Games.
Pre-Olympic test events also must be held at the 75,000-seat stadium.
If the roof is not in place by the deadline, the partially finished project could loom over the stadium as an embarrassing symbol of the delays that have plagued almost every aspect of the city's preparations.
Last month, Oswald said April 28 was the last possible date for the huge roof arches to be moved into place, though a May 9 deadline was later added before alternative "contingencies" would be demanded.
Crews have started laying the tracks for the operation, but it was unclear when it could begin.
"The sliding is slightly later than expected," Oswald said, adding that work to install the glass on the roof was being done earlier to compensate for the holdup.
Oswald made no mention of next week's deadline or dates for test events.
"We've made up for lost time and we will host the world with state-of-the-art facilities," said Gianna Angelopoulos-Daskalaki, the head of the Olympic organizing committee.
The stadium site is part of a frantic push to finish Olympic projects with less than four months to go before the opening ceremony.
Greece's deputy culture minister, Fani Palli Petralia, said crews are working "triple shifts at all sites" to get the facilities ready with less than four months to go before the start of the Games.
The IOC is also highly concerned about the pace of work at two rail projects and whether organizers will finish a fiber optic network needed for full television coverage.
But Transport Minister Michalis Liapis assured the IOC team that the rail lines and the TV cables would be ready.