WASHINGTON — Home prices rose in nearly all major U.S. cities in April from March, further evidence of a housing market that is slowly improving even while the job market slumps.

The Standard & Poor’s/Case-Shiller home price index released Tuesday showed increases in 19 of the 20 cities tracked. That’s the second straight month that prices have risen in a majority of U.S. cities. And a measure of national prices rose 1.3 percent in April from March, the first increase in seven months.

San Francisco, Washington and Phoenix posted the biggest increases in April. Prices fell 3.6 percent in Detroit, the only city to record a drop.