The number of available jobs in the U.S. exceeded the number of job seekers by more than 650,000 in July—a gap that has been growing—in a sign of an increasingly tight labor market that is altering how employers find workers.

The number of available jobs in the U.S. rose by about 117,000 to a seasonally adjusted 6.94 million in July, the Labor Department said Tuesday. That is the highest level on record back to 2000, exceeding the prior peak set in April. It also exceeds the 6.28 million Americans who were unemployed during...