John Sharkey, who insisted the Hydro in Glasgow had been back on track for completion by the end of August before a fire broke out in roof space at the site in June, said: "It really is going to be right down to the wire on it."
Mr Sharkey cited a possibility of rescheduling dates of acts but emphasised the focus was on getting the building completed.
Asked if the Scottish Exhibition and Conference Centre might have to pay compensation to acts booked into the Hydro if the building were not ready on time, Mr Sharkey replied: "The thing about it is we basically need to look after our promoter relationships. We just need to find a solution to make it work.
"There is some degree of sympathy that has come around as a result of the fire. If we can reschedule dates, we might be looking at that.
"At the moment, we are not even looking at that. We are just looking at getting the building finished."
Asked whether he would assign a percentage probability to the Hydro being finished on time for Rod Stewart's opening concert planned for September 30, Mr Sharkey replied: "I am not going to. As things stand at the moment there is a lot to do but we are not cancelling the opener because we think we can do it.
"There has been a hell of a lot done in a short period of time. It is still moving at pace."
It is understood that, earlier this year, amid serious worries over whether the Hydro would be completed in time for its planned September opening, the SECC entered into agreements to incentivise contractor Lend Lease to complete the job on time.
Mr Sharkey declared yesterday that, by the time of the fire, completion had been on track for the end of August.
The SECC chief, who estimated damage caused by the fire at up to £5 million, said: "We were looking to complete by the end of August. We then had the fire on June 8.
"Whereas we had a bit of leeway, we are (now) going to be absolutely to the wire in getting the building open on time."
He added: "It is looking pretty decent, tidy, inside. We are really going to be on a bit of a hairy journey right up to the end of September."
Mr Sharkey highlighted a planned hectic opening week for the Hydro, with Rod Stewart scheduled to play four nights, and Jesus Christ Superstar, Fleetwood Mac and Bruno Mars also booked in.
He acknowledged there were still differences with Lend Lease over the final bill.
However, he said: "We are still squaring down the final account. There isn't a material difference between us."
It is understood sub-contractors have until the end of August to complete their work on the Hydro, a timescale which will allow commissioning work to take place ahead of the planned September 30 opening.
Mr Sharkey noted Lend Lease and SECC would now have to work "over the top of one other" during commissioning.