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

The Standard & Poor’s/Case-Shiller home price index shows 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. Prices fell 3.6 percent in Detroit, the only city to record a drop.

The month-to-month prices aren’t adjusted for seasonal factors. Still, prices in half of the cities are up over the past 12 months.

Prices are increasing as other parts of the housing market are strengthening. Sales of new and previously occupied homes are up over the past year, in part because mortgage rates have plunged to the lowest levels on record. Builders are more confident and are starting to build more homes.

The S&P/Case-Shiller monthly index covers roughly half of U.S. homes. It measures prices compared with those in January 2000 and creates a three-month moving average. The April figures are the latest available.

Its measure of home prices for all 20 cities fell 1.9 percent over the 12 months ending in April. That suggests weaker markets continue to weigh on national prices.

But other measures show home prices have risen nationally over the past year. CoreLogic, a private firm, calculates that prices rose 1.1 percent nationally in the 12 months ending in May. Federal Housing Finance Agency, which oversees mortgage giants Fannie Mae and Freddie Mac, says prices have increased 3 percent in the 12 months ending in April.

Recent data indicate that the housing market has started to recovery more than five years after the bubble burst.