At least four people have died after contracting a severe respiratory illness that has spread to more than 40 states, public health officials announced on Wednesday.

The deaths were the first to be linked to the nationwide outbreak of enterovirus 68, which has caused an influx of sick children — some of them critically ill — at hospitals around the country. The Centers for Disease Control and Prevention confirmed 472 cases of the infection as of Wednesday, although experts said the true number of cases was likely to be many times that number.

Tests showed that four patients who died had been carrying the virus, but it was unclear to what extent the virus contributed to their deaths, the C.D.C. said.

One of them was a 10-year-old girl from Cumberland, R.I. Her parents took her to a hospital last week because she had difficulty breathing and symptoms of a common cold. Within 24 hours of being admitted she began to deteriorate rapidly, and she died a short time later, said Dr. Michael Fine, the director of the state’s Health Department.