The Mortgage Bankers Association said its seasonally adjusted index of mortgage application activity, which includes both refinancing and home purchase demand, rose 0.3 percent in the week ended Oct. 11. That follows a gain of 1.3 percent in the week ended Oct. 4.
The figures come as the U.S. federal government shutdown has cast a spotlight on fiscal policy, with some economists worrying that the stalemate in Congress could drag on the economy.
That shutdown affected the mortgage market, MBA said.
"Purchase applications for government programs dropped by more than 7 percent over the week to their lowest level since December 2007, and the government share of purchase applications dropped to its lowest level in almost three years," Mike Fratantoni, MBA's vice president of research and economics, said in a statement.
MBA data showed 30-year mortgage rates edged up 4 basis points to 4.46 percent, but rates were still down from September when they matched the 4.8 percent high for 2013.
The refinancing index gained 3.3 percent after recently hitting the lowest level since June 2009. In contrast, the gauge of loan requests for home purchases, a leading indicator of home sales, fell 4.8 percent.
The mortgage survey covers more than 75 percent of U.S. retail residential mortgage applications, according to MBA.