TOKYO, March 15 (Reuters) - A Japanese state-backed fund said on Tuesday it sold its entire stake in robotics startup Groove X, which makes an "affectionate" companion robot, to a fund owned by Japanese fashion billionaire Yusaku Maezawa.

The state fund, INCJ, four years ago invested 3.5 billion yen ($29.6 million) in Groove X, which was founded by an alumni of SoftBank Group Corp's robotics unit. It did not disclose the price of the sale to the Maezawa fund and declined to say if it made a profit.

Maezawa "showed a strong interest in the concept of a home robot as providing a solution to social issues," INCJ said in a statement giving its rationale for the exit.

The Lovot, an amalgam of "love" and "robot", has wheels and resembles a penguin with cartoonish human eyes. It has interchangeable outfits and communicates in squeaks.

Groove X in the past raised funds from investors such as a Toyota Motor Corp-backed fund and chat app operator Line Corp.

Maezawa, who late last year visited the International Space Station on a Russian rocket, made his fortune founding the online fashion retailer Zozo which was bought by SoftBank's internet business.

Through his fund Maezawa has invested in ventures including one making smart cat-litter trays which analyse toilet habits and track animal health and another that offers personalised videos from celebrities. ($1 = 118.3100 yen) (Reporting by Makiko Yamazaki; editing by Richard Pullin)