The inflation rate rose 2.4% in May compared to the previous year, a 0.1% increase from the previous month. Economists had expected to see tariff-related price increases in the May report, leading to questions over whether an inflationary price bump is still to come in the summer or if low consumer demand is responsible for modest price increases.

Average rates are likely to stay in the 6.75% to 7.25% range unless the Fed signals multiple cuts and backs up their policy with data, said Nicole Rueth, of the Rueth Team with Movement Mortgage. "Homebuyers waiting on rates to drop drastically might be disappointed," Rueth said.

Mortgage rates moved down this week, with the 30-year fixed rate averaging 6.86 percent, compared to 6.90 percent the previous week, according to Bankrate’s latest lender survey.