A measles outbreak that has spread over a swath of West Texas, killing one child, shows no signs of slowing, according to data announced on Tuesday by state health officials.

The Texas Department of Health reported that since late January, nearly 160 people have contracted measles — 20 more cases than reported on Friday — and 22 have been hospitalized.

The Centers for Disease Control and Prevention announced on Tuesday that it would send some of its “disease detectives” to Texas, one of the first steps the new administration has taken to help manage the outbreak.

The news comes amid criticism of federal officials for underplaying the need for immunizations with the measles-mumps-rubella vaccine, one of the most important tools in quelling an outbreak.

Robert F. Kennedy Jr., the health and human services secretary and a prominent vaccine skeptic, published an opinion piece on Sunday night acknowledging that vaccines protect children from measles and urged parents to talk with their doctors “to understand their options to get the M.M.R. vaccine.”

“The decision to vaccinate is a personal one,” he wrote.

In a prerecorded interview that aired on Fox News on Tuesday, Mr. Kennedy said that the federal government was shipping doses of vitamin A to Gaines County, in West Texas, and helping to arrange ambulance rides.