Canalside’s historically aligned canal project on the old Memorial Auditorium site, which will include reflecting pools during the summer and become ice skating rinks during the winter, was supposed to be finished last Thanksgiving.

The completion date later was moved to this spring, and then to the end of this year. Now the finish line is up in the air.

Construction could soon skid to a halt – pushing the completion date into 2014 – due to a rift between the general contractor and a state agency overseeing waterfront development.

Erie Canal Harbor Development Corp. earlier this month notified the contractor for the $20 million project that it intends to remove the company from the job because of delays. Thomas Dee, the agency’s president, in a letter accused DiPizio Construction Co. of failing to maintain the project schedule, provide required materials as necessary and coordinate work by subcontractors.

“ECHDC and its consultants have repeatedly advised your firm of its deficient work and taken all reasonable steps to ensure the work can be completed in a timely and efficient manner. ... Despite these efforts, DiPizio has failed to demonstrate any significant improvement in its performance, necessitating the actions taken here,” Dee wrote.

DiPizio Construction countered in court documents that it was being made a scapegoat to deflect attention from the agency’s shortcomings. The company is hoping to stay on the job, and it says it can finish by Nov. 1 – nearly a year later than the waterfront agency envisioned. The contractor has also launched a lawsuit to recoup losses in the event it is dismissed.

Both sides will appear June 5 before Judge Timothy J. Walker in State Supreme Court, where the construction company – which for now remains on the job – will seek a preliminary injunction to halt the agency’s effort to remove it from the site.

If the injunction is not granted and the waterfront agency doesn’t change its mind, the company will be given a three-day notice to vacate the site, and the construction project will grind to a halt.

In his letter to DiPizio, Dee cited a Jan. 24 report compiled by Liro Engineering that reviewed DiPizio’s work and offered ways to reduce delays and make improvements. The recommendations, he wrote, still failed to “demonstrate any significant improvement in its performance.”

But none of the delays could be laid on the company’s doorstep, DiPizio countered through attorney Michael E. Ferdman. It called the reasons for termination “vague and easily disputed.”

“The Notice of Termination is a political document, issued to cover up the real truth about this project: the bad faith administration of the construction agreement by the defendant respondent, needlessly forcing long delays and driving up not just DiPizio Construction Co.’s costs, but taxpayers’ costs,” Ferdman wrote.

He warned that the company – which he said has an excellent reputation within the industry and a 35-year history of working on state projects, in which nothing like this has occurred before – could “suffer irreparable damage” if terminated. He said termination could also result in pink slips for 60 construction workers.

DiPizio Construction was supposed to begin work in February 2012, but work was held up until May because of delays in state funding. The 300-day timetable to complete the project was interrupted due to winter weather between Dec. 1 and March 1, when the ground thawed and the air was warm enough to pour concrete.

The company maintains that delays beyond its control – delays for which it blames the waterfront agency – have now pushed the timetable to late fall.

It’s not clear how long it will take the waterfront agency to get the project back on track if DiPizio Construction is off the job.

Pete Gallivan, a spokesman for Gov. Andrew M. Cuomo, declined to comment, with the project in litigation.