UPDATE 2-Ford sees market share gains, increases production

* Ford sales seen down 10-20 pct in June vs year ago

* Industry sales seen down 25-30 pct in month -- analyst

* U.S. June auto sales at 10 mln unit annual rate possible

* Ford increasing Q3 North America production by 5.4 pct

* Ford shares rise 3 percent (Recasts first paragraph, adds Ford increasing North American production)

By David Bailey

DEARBORN, Mich., June 29 (Reuters) - Ford Motor Co (F.N) said on Monday it expects to gain U.S. market share in June as its sales would hold up much better than the rest of the industry and signaled its increasing confidence by raising production.

Ford said it would increase North American production in the third quarter by about 5.4 percent from a plan disclosed in early June amid signs that demand has begun to stabilize.

That plan had set Ford's first year-over-year quarterly production increase in North American in two years.