WASHINGTON, July 9 Rent and housing costs are keeping U.S. inflation higher than preferred but consumer price pressures will continue to come down over time, Treasury Secretary Janet Yellen said on Tuesday, as a top White House adviser cited what she called "tremendous progress" in bringing down inflation.

Yellen told the U.S. House of Representatives Financial Services Committee that inflationary factors including supply issues and labor market tightness have eased, which would help continue to drive down consumer price pressures.

"I believe that it (inflation) will continue to come down over time. Rents and housing costs continue to leave it higher than we would ideally like," Yellen told the U.S. House panel on financial services.

"Although the labor market was initially very tight, now we have a strong labor market, but one with fewer pressures that would create inflationary concern, so inflation is coming down," she said.

Lael Brainard, chair of the White House National Economic Council and a former vice chair of the Federal Reserve, said the Biden administration is encouraged by continued progress on lowering inflation, but President Joe Biden would keep fighting to lower the cost of living for working families.

Brainard said several months of data had confirmed that inflation was returning to the Fed's 2% target, noting that the most recent data showed an inflation level of 2.6%, which she said marked "tremendous progress."

The inflation target is set in reference to the Personal Consumption Expenditures price index, which as of May was increasing at a 2.6% year-over-year rate.

Looking more closely at the underlying categories of inflation showed an actual reduction in food prices, and gasoline prices holding steady at around $3.50 a gallon over the July 4 "driving holiday," Brainard added.

"But we also know that Americans are still squeezed by the cost of living," Brainard said. She said Biden would continue to push for more affordable housing, slower increases in rents and the introduction of tax credits to help first-time homeowners.

The Fed receives consumer price information for the month of June on Thursday. The consumer price index did not rise at all in May, and analysts anticipate another weak reading later this week.