WHITE PLAINS, N.Y.—Democratic presidential nominee Hillary Clinton said she was feeling much better after a pneumonia diagnosis and promised to release additional medical records this week, moving to contain concerns about her well-being and forthrightness after she stumbled exiting a 9/11 ceremony.

The pneumonia diagnosis, belatedly disclosed by her campaign Sunday, has taken Mrs. Clinton off the road and off-message just as her campaign was working to focus on her agenda. Instead of campaigning and fund-raising in California,...