“We strive,” he added, “to make that fraction even lower.”

Holly Hart of Gray, Tenn., said she was recently reading while her 3-year-old daughter was in the room when she noticed that Disney Junior characters in the video her daughter was watching started “turning into monsters and trying to feed each other to alligators.” An image previewing a recommended video showed the characters in a provocative pose.

“It was an eye-opener for me,” said Ms. Hart, who had downloaded the app because it was being used at the local elementary school.

Not all of the inappropriate videos feature cartoons. Alisa Clark Wilcken of Vernal, Utah, said her 4-year-old son had recently seen a video of a family playing roughly with a young girl, including a scene in which her forehead is shaved, causing her to wail and appear to bleed.

Most of the videos flagged by parents were uploaded to YouTube in recent months by anonymous users with names like Kids Channel TV and Super Moon TV. The videos’ titles and descriptions feature popular character names and terms like “education” and “learn colors.”

They are independently animated, presumably to avoid copyright violations and detection. Some clips uploaded as recently as August have millions of views on the main YouTube site and run automatically placed ads, suggesting they are financially lucrative for the makers as well as YouTube, which shares in ad revenue. It is not clear how many of those views came on YouTube Kids.

One video on YouTube Kids from the account Subin TV shows the “PAW Patrol” characters in a strip club. One of them then visits a doctor and asks for her cartoon legs to be replaced with long, provocative human legs in stilettos. The account’s description says, “Video created with the purpose of learning and development of children!”

The account that posted the video seen by Ms. Burns’s son is named Super Ares TV and has a Facebook page called PAW Patrol Awesome TV. Questions sent there were mostly ignored, though the account did reply: “That’s a Cute character and video is a funny story, take it easy, that’s it.”