"Mortgage rates fell for the third straight week following signs of cooling inflation and market expectations of a future Fed rate cut," said Sam Khater, Freddie Mac's chief economist, in a press release. "These lower mortgage rates coupled with the gradually improving housing supply bodes well for the housing market."

Zillow's rate tracker put the 30-year FRM at 6.56% as of 11:45 on Thursday morning, up 2 basis points on the day but down 3 basis points from the prior week's average.

Meanwhile, data from Lender Price posted on the National Mortgage News website put the 30-year FRM 2 basis points higher than where it was last week, at 6.86% versus 6.84%.

At the same time, the 10-year Treasury yield was up 5 basis points on the day, to 4.27%. On June 13, it closed at 4.23%, but bounced up and down between a low of 4.19% and a high of 4.30% over the next week.

While the FOMC passed on a rate cut at its last meeting and made statements on the possibility of future actions, the market consensus is that it will act at Sept. 18 meeting, Louis Navellier, an investment banker said, adding "but I also believe that the Fed should cut key interest rates on July 31."

But if bond vigilantes drive Treasury yields lower, then the Fed may be forced to cut key interest rates sooner than later," Navellier said.

The markets are back to data watching, said Melissa Cohn, regional vice president of William Raveis Mortgage.

"There were no huge surprises in the Fed's comments or dot plot," Cohn said in a statement. "Expecting one rate cut should be neutral for the markets, and the Fed's future actions will depend on the markets."

Next month's Consumer Price Index report holds the key for what the FOMC will do. If it shows further progress in terms of reducing inflation, "then we will have a good summer for mortgage rates and the real estate market," Cohn said.