The Mortgage Bankers Association said its seasonally adjusted index of mortgage application activity, which includes both refinancing and home purchase demand, rose 1.3 percent in the week ended Oct. 4. That follows a dip of 0.4 percent in the week ended Sept. 27.
The figures come as a 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.
MBA data showed 30-year mortgage rates slipped 7 basis points to 4.42 percent, after in September matching the 4.8 percent high for 2013.
The refinancing index gained 2.5 percent after recently hitting the lowest level since June 2009. The index is now at its highest since early August.
The mortgage survey covers over 75 percent of U.S. retail residential mortgage applications, according to MBA.