CAMBRIDGE — An emotional debate over the fate of a Martin Luther King Jr.-themed mural on a condemned school building named for King has evolved into a pledge by the city to take a more active role in caring for its schoolhouse art.

Demolition of the Martin Luther King Jr. School on Putnam Avenue is scheduled to begin within weeks, and a new school of the same name will be erected on the site. For several months, Cambridge-based artist David Fichter and an alliance of parents, former students, and teachers contended with officials over the city’s seeming unwillingness to promise a home for the mural, titled “Furthering the Dream,” on or in the new building.