WASHINGTON  Millions of households will lose television reception next week when about 1,000 broadcasters around the nation shut off their analog signals and complete their conversion to digital programming, federal officials say.

The government has spent more than $2 billion to ease the transition to digital television, and in the last few months has cut in half the number of households that are unprepared for the final conversion on June 12. But the latest survey by the Nielsen Company indicates that as of the end of May, more than 10 percent of the 114 million households that have television sets are either completely or partly unprepared.

Michael J. Copps, the acting head of the Federal Communications Commission, said that the people most likely to lose reception are society’s most vulnerable  lower-income families, the elderly, the handicapped and homes where little or no English is spoken. The transition will also hit inner-city and rural areas hardest, he said.

“We are much better prepared than we were in February, when the original transition was to have occurred, but there will nonetheless be significant disruptions,” Mr. Copps said in an interview. “In the past five months we’ve tried to accomplish what should have been done over the last four years.”