US single-family homebuilding and permits for future construction fell sharply in September as higher mortgage rates suppressed demand, suggesting residential investment resumed its declining trend in the third quarter.

Single-family housing starts, which account for the bulk of homebuilding, dropped 4.6% to a seasonally adjusted annual rate of 859,000 units last month, the Commerce Department's Census Bureau said on Tuesday. Single-family building permits decreased 4.0% to a rate of 845,000 units.

Mortgage rates have surged in recent weeks, with the 30-year fixed rate averaging 7.40% last week, the highest level in nearly three years, data from mortgage finance firm Freddie Mac showed. The higher borrowing costs are tracking Treasury yields as the US-Israeli war with Iran fans inflation.

A National Association of Home Builders survey on Monday showed sentiment among single-family homebuilders plunged in October to the lowest level since June 2012. The NAHB blamed rising material costs and mortgage rates as well as more expensive diesel and "worsening" labor conditions amid an immigration crackdown for the deterioration in sentiment.

Slumping sales have led to a glut of unsold houses on the market, further reducing the incentive for developers to break ground on new single-family housing projects. Despite the overhang of new single-family homes, there is a national housing shortage, which is keeping home prices elevated.

Housing affordability has dominated campaign messaging ahead of the November 3 midterm election, which will determine control of Congress. President Donald Trump earlier this year refused to sign a bipartisan housing affordability bill, calling it "a big yawn" as he pressed Congress, including fellow Republicans resisting his demands, to first pass separate and contentious voting requirements.

Residential investment rebounded in the second quarter, also reflecting renovations, making a small contribution to gross domestic product. The rise followed five straight quarterly declines.