ST. PETERSBURG — Demolition will go forward of two historic buildings on prime downtown property considered ripe for redevelopment.Preservationists, who sued to save the buildings on Central Avenue's 400 block, have agreed to drop their lawsuit. The announcement came Thursday evening, minutes before City Council members were to vote on a request by St. Petersburg Preservation to designate the former Pheil Hotel and Theater and Central National Bank as local landmarks."It is time to move forward … and work with St. Petersburg Preservation to protect what makes the Sunshine City special," Mayor Rick Kriseman said in a statement.St. Petersburg Preservation had worked hard to reach a resolution, vice president Peter Belmont said."It is difficult to accept the loss of buildings that represent an important piece of St. Petersburg's history, but we are convinced the result will be a positive," he said in a joint statement with the city.In April, the preservation group, whose mission is to "keep St. Pete special," filed a lawsuit to overturn a city decision giving the owners permission to demolish the two early 20th century buildings. The group argued that St. Petersburg erred in granting the demolition request based on an exemption to city codes. As part of the agreement, the city says it is committed to an ordinance change that will disallow the type of demolition exemption preservationists fought.The buildings sit in a block that stretches from Central Avenue to First Avenue S, and Fourth Street to Fifth Street. Until recently, the property had been caught up in a legal snarl over ground leases between First States Investors, a real estate investment trust, and descendants of an early St. Petersburg mayor, Abram C. Pheil. The two parties recently ended their dispute and the run-down property, vacant since 2006, was put on the market.But the agreement came with conditions. First States attorney Don Mastry said the settlement was "expressly conditioned upon the buildings being demolished." If demolition was not allowed, he and the Pheil family said, the block would remain undeveloped and the buildings would continue to deteriorate until 2058 — when the leases expired. As a result of Thursday's agreement, First States has pledged to work with St. Petersburg Preservation and will donate $100,000 to the group's cause.Mark Stroud, the Pheils' broker, said there's already a buyer for the 2.3-acre property.St. Petersburg Preservation had argued that the buildings should be saved because of their historic value. Their "splendor," the group said on its website, is obscured by the "cheese grater" aluminum grill work that was installed in the 1960s. Its removal, the group said, would bring the buildings "back to life."