SAN DIEGO — California recorded its strongest August for home sales in three years as prices climbed modestly, a research firm reported Tuesday, providing fresh evidence of sustained gains in the housing market.

An estimated 43,542 new and existing houses and condominiums sold last month, up 5.6 percent from 41,247 sales in July and up 5.2 percent from 41,387 during the same period a year earlier, CoreLogic Inc. said. It was the highest August sales tally since 2013.

The median sales price was $432,000, barely changed from $430,000 in July and up 5.8 percent from $408,500 August 2015. It was the 54th straight month that prices have increased from a year earlier, though gains have moderated over the last two years.

In Southern California, job growth and low interest rates helped propel the six-county region to its highest August sales in a decade, said CoreLogic analyst Andrew LePage. The region had 23,278 sales in August, up 8 percent from 21,557 sales in July and up 9.5 percent from 21,263 sales in August 2015.

Southern California’s median sales price was $465,000, matching a nine-year high set in June and July and up 6.2 percent year from $438,000 a year earlier.

Gains in the San Francisco Bay area were more tempered, according to CoreLogic. Sales in the nine-county region reached 8,374 homes, up 8.3 percent from 7,729 sales in July and up 3.2 percent from 8,113 sales a year earlier.

The median home sales price in the Bay area was $675,000, a second straight monthly decline after hitting an all-time high of $710,000 in June. The sale price was down 2.9 percent from $695,000 in July but up 5.2 percent from $641,750 a year earlier.

The California Association of Realtors said last week that affordability constraints and tight supplies hampered sales in August, particularly in the high-cost Bay area.

The group said California had a 3.4-month supply of unsold single-family homes, well below a normal supply of five to seven months. Supplies were tighter in the Bay area.