Supermarket giant Stop & Shop has backed out of its plans to develop an anchor store at Trinity Financial’s mixed-use project on Boston’s Rose Kennedy Greenway, focusing its attention on an unnamed rival site.

Now Trinity is going back to the drawing board, seeking another supermarket operator to anchor its planned project, One Canal, on three parcels owned by the Massachusetts Department of Transportation (MassDOT) and the Massachusetts Bay Transportation Authority.

Quincy-based Stop & Shop, which was widely supported by adjacent residents in the city’s North End and West End, is now "concentrating on occupying another site in the neighborhood," according to a statement from Trinity.

"We are disappointed at this turn of events, especially after we had been having detailed discussions with Stop & Shop since last fall and believed we had essentially reached an agreement," said Sarah Barnat, senior project manager for Trinity Financial. "Nevertheless, we remain optimistic about the future development of this complicated site, even if it means finding another appropriate supermarket operator to serve the neighborhood."

The background on the disposition of the site, made up of land known as Parcels 2A, 2B, and 2C, is complicated. In 2005, Trinity Financial was one of the bidders for the site when the Massachusetts Turnpike Authority and the MBTA issued invitations to bid on these and four other parcels in the Bulfinch Triangle Area.

Trinity won the right to develop a nearby parcel, Parcel 1A, but was unsuccessful in securing designation on the three parcels along North Washington Street. Hines Raymond, a joint venture of Raymond Properties and the Hines Co. of Houston, were chosen and, though initially lacking a supermarket component in its plan, were directed to include one. After Hines Raymond experienced delays in a faltering economy and was de-designated last summer, Trinity Financial was invited by officials of the MBTA and MassDOT, successor to the Turnpike following a transportation agency consolidation, to step in. Hines Raymond had proposed a significant amount of office space for the site.

Trinity had been the successful bidder in 2005 on Parcel 1A and had completed the successful Avenir development, including 241 units of rental housing, which it later sold to the residential real estate firm Archstone Smith. To date, the Avenir project is the only project completed on any of the seven Bulfinch parcels offered for development.

Trinity Financial’s Barnat said in a statement that both Trinity’s original and current plans for the North Washington Street site call for a residential use above two floors of retail, one of which would be dedicated for supermarket use.

"The site definitely has its challenges, with a vent shaft and transformers and with the Green and Orange Lines, and the Central Artery running underneath it. But we are not afraid of challenges," she said in a statement.

In a written statement, Barnat acknowledged the neighborhood might not be able to support two supermarkets. However, she added, "The community has been wanting a supermarket for years and years. We have heard them, and we hope to be the team who can finally deliver one."

A spokesperson for Stop & Shop declined to comment.