The index that assigns 1985 a base value of 100 fell from 64.4 to 62, the Conference Board said.
The monthly Consumer Confidence Index is based on a survey of 5,000 households.
In May, consumers were less confident about current business conditions. In addition, the Expectations Index dropped from 77.3 to 72.3.
"Consumers were somewhat more positive about current conditions, but slightly more pessimistic about the short-term outlook. Income expectations, which had improved last month, declined in June," said Lynn Franco, director of the Conference Board Consumer Research Center.
She said the numbers indicate the pace of economic activity will show little change in the near-term.
In June, the number of respondents to the survey indicating economic conditions were "good" rose from 13.6 percent to 14.9 percent. The percentage of respondents indicating conditions were "bad" also rose, climbing from 34.7 percent to 35.1 percent.
On the employment front, the percentage of consumers indicating jobs were "plentiful" rose from 7.5 percent to 7.8 percent, while the percentage indicating jobs were "hard to get" rose from 40.9 percent to 41.5 percent.