WASHINGTON (Reuters) - U.S. mortgage rates increased for a fourth straight week this week, suggesting the housing market could remain on the back foot for some time even as the Federal Reserve cuts interest rates.

The average rate on the popular 30-year fixed-rate mortgage rose to 6.54% from 6.44% last week, mortgage finance agency Freddie Mac said on Thursday. It averaged 7.79% during the same period a year ago.

Mortgage rates initially fell in September, dropping to more than a 1-1/2-year low by the end of the month as the Fed began lowering rates. They have risen as solid economic data, like retail sales and annual revisions to national accounts, forced traders to abandon hopes for another 50-basis-point rate cut from the U.S. central bank next month.

"The continued strength in the economy drove mortgage rates higher once again this week," said Sam Khater, Freddie Mac's chief economist. "Over the last few years, there has been a tension between downbeat economic narrative and incoming economic data stronger than that narrative."