A planned 52-story Copley Place residential tower will be delayed — and could be completely canceled — because of rising construction costs and concerns over the rising supply of luxury housing in Boston, Simon Property Group said.

“Simon has elected not to proceed at this time with the construction of The Copley residential tower since construction pricing in Boston continues to escalate and there are a number of new projects already under construction or soon to be under construction,” a Copley Place spokeswoman said.

In an earnings call on Wednesday, Simon Property Group’s chief executive David Simon referred to “our likely decision to postpone the construction of the Copley Residential Tower, due to the rapidly rising construction cost and our beginning concerns around supply and demand in the Boston residential market.”

The tower — which was to feature 421 apartments and 121 condos, and 45,000 square feet of more retail and restaurant space — was part of a $500 million expansion, announced in August 2015.

Copley Tower was to join a slate of planned and current high-end residential towers, which are rapidly changing the skyline and demographics across Boston’s downtown.

“We do have to worry about supply and demand. And I’m not worried about supply and demand in our retail portfolio. In the case of Copley I got nervous about it,” Simon said.

He told investment analysts: “I mean, I would encourage everybody to study what’s going in construction cost and what’s going on in supply and demand there. … The reality is, when we started seeing the construction cost, it just not the right time to do it with all the supply and the cost there.”

Simon Property last December had said they also intended to renovate the property and add more space for luxury retailers and restaurants at the upscale shopping mall, hotel and office complex. The entire face of the outside area on Dartmouth Street, between the mall and Tent City apartments, was to be redone.

On Wednesday, Simon told analysts some parts of the project will proceed.

“Work will continue on redeveloping and modernizing the existing retail space at the center as well as the development of the Southwest Corridor, which will create a new entrance to Copley,” he said. “We expect this work will enhance the shopping experience for our guests and retailers and further strengthen our position in the heart of Boston and will be completed by summer of ‘17.”

He also did not rule out one day building the tower.

“Assuming we make the decision to postpone, it does not foreclose the opportunity to build the tower in the future as market conditions warrant,” he told analysts.

Copley Place opened in 1983, and Simon’s ownership dates to 2002. It currently has about 370,000 square feet of retail space anchored by Neiman Marcus and Barneys New York.