A day after being shot in the head by a masked gunman, Gary Melius, a well-known Long Island developer and prominent political patron, was recovering on Tuesday, and remarkably lucid.

He issued a statement about his “near-death experience,” and talked to the police. But he could not provide the answer to the question they both wanted to know: Who shot him?

Mr. Melius, 69, told the police that he did not know or recognize the masked gunman who ambushed him outside his opulent estate, the Oheka Castle on Long Island’s Gold Coast. So on Tuesday, detectives continued their pursuit of the shooter and of any clues as to who might have had a motive to carry out the midday attack.

Could it have been tied to his role as a political power broker? Mr. Melius has donated hundreds of thousands of dollars to both Democrats and Republicans over the years. His Monday night poker games, held at the castle in Huntington, drew the famous and the well-connected, and his circle of intimates included senators, congressmen and local politicians.