Company researchers have already experimented with around 200 alternatives. Among them, Ms. van der Puil said, was a substance called PLA, one of the few bio-based plastics that are readily available. Lego is also already using polyethylene made from sugar-cane husks in flexible pieces like dragon wings, palm trees and fishing rods, but these constitute only 1 percent to 2 percent of its output, and the material is too soft for the company’s toy blocks.

Most test materials, both bio-based and recycled, have so far fallen short. Some bricks made with the new materials have broken, leaving sharp edges that could injure a child, or have popped out with ugly, muddied colors. Others have on occasion produced misshapen or pockmarked bricks.

The search for a substitute for petroleum-based plastic could yet take years of work, Mr. Brooks acknowledged. Still, executives argue that, as a company that models itself as a de facto educator as much as a profitable enterprise, it has little option but to keep trying.