WASHINGTON—More than 57 million Americans have become ill from the H1N1 influenza virus and nearly 11,700 have died, according to estimates released Friday by the Centers for Disease Control and Prevention.

While the new figures show the H1N1 pandemic virus is still spreading, they also reflect a slowdown in the transmission of the illnesses since last fall. The CDC had last estimated about 55 million Americans had been sickened, 246,000 were hospitalized and about 11,100 had died through mid-December.

The...