Rare earth element map: In 2013, China produced about 90% of the world's supply of rare earth element ores. The USGS Mineral Commodity Summary [2] reported production tonnages for Australia, the United States, India, Brazil, Russia, Vietnam, and Malaysia. Rare earth element exploration and/or development is being done in Canada, South Africa, Thailand, Malawi, and Sri Lanka; however, production from those countries was insignificant during 2013.
http://geology.com/articles/rare-earth-elements/
Further China has already show willingness to ban export of these materials (for example in 2010). At the end of the day the risk to the production of batteries in particular has motivated vulnerable countries like Japan to develop alternative processes:
http://fortune.com/2016/07/12/honda-rare-earth-battery-hybri...
China comes number four on the list of lithium producing companies.
Much of the world's lithium reserves seem to come from South America.
http://investingnews.com/daily/resource-investing/energy-inv...