According to the agency's consumer price index, the regions saw a 4% increase from last year.
There are rules in place to protect renters during the coronavirus pandemic.
LA rent relief program to begin registration for tenants financially impacted by COVID-19
A recent survey found that only 82% of renters in Los Angeles and Orange counties paid their full rent last month.
People who rent have largely been able to survive the initial months of the pandemic helped by unemployment and federal relief checks. But the extra $600 in unemployment benefits ceases at the end of July and local eviction moratoriums are expiring. There is no agreement between the White House and Congress on a second federal relief package.
More broadly, there are fewer supports in place for renters than for homeowners. And as a jump in virus cases in numerous states nationwide adds more uncertainty to the economy and job market, many who rent are facing a precarious future.
"It's an incredibly stressful situation for renters," said Bruce McClary, spokesman for the National Foundation for Credit Counseling, a nonprofit that works directly with consumers. "I don't know what lies in the road ahead."
The Associated Press contributed to this report.