A video released by team members shows them using it to control a handset by pinching, squeezing and prodding it to zoom in or out, and carry out other functions.

It could also be used in the future to interact with a virtual avatar.

Project leader Marc Teyssier said he understood why some people found it creepy.

"I do think it's creepy - I get it," he told the BBC.

"We are not used to human touch on objects. This project has made people reflect on what technology is and why this is creepy."

Tickling the skin on the back of the phone could release a laughing emoji in a message, for example, while a pinch could result in an expression of anger.

Writing on the project website, Mr Teyssier said the "cold interface" of a smartphone "doesn't allow natural interaction and input".

The skin consists of two different forms of silicone layers, and electrodes attached to a hardware controller.

Mr Teyssier told New Scientist that getting the right balance of materials was difficult.

"The constraint was to develop something that was stretchable and that can also detect touch," he said.

He also said that make-up or paint could be used in order to "increase anthropomorphism".

There are no plans to market the case, although Mr Teyssier has published how it was made.

"Anyone can reproduce it," he said.

The materials are mass-produced and each unit would cost less than £5 to build, he estimated.

The team also adapted it to fit other portable electronics, such as a smart watch, companion robot, and laptop launchpad.

On social media it has been greeted with a degree of fascination and horror, with many agreeing that the Skin-On case was decidedly "creepy".

"This is profoundly wrong and I want one immediately," tweeted lecturer Belinda Barnet.

The research paper on "Skin-On interfaces" has been published at the ACM Symposium on User Interface Software and Technology, taking place in Louisiana.