A bipartisan group of senators introduced a plan Tuesday to reform the housing finance system and wind down the government-sponsored enterprises Fannie Mae and Freddie Mac.

Eight members of the Senate Banking Committee, including both Republicans and Democrats, proposed creating a new agency modeled after the Federal Deposit Insurance Corporation to provide backstop insurance for mortgage-backed securities. The agency, which would be called the Federal Mortgage Insurance Corporation or FMIC, would be funded with premiums from private loan issuers. It would require investors to hold 10 cents for every dollar at risk, and only provide insurance payouts after a substantial amount of private capital was exhausted.