Private insurers are considering a request by U.S. officials to guarantee mortgages for veterans—the fastest-growing part of the market.

The U.S. Department of Housing and Urban Development is urging mortgage insurers that rely on Fannie Mae and Freddie Mac for business to offer supplemental protection for lenders to military members and veterans. Only 25 percent of VA loan amounts are backed by the Department of Veterans Affairs, a limit that keeps some firms from fully participating in the program, Ginnie Mae President Ted Tozer said.