The Senate has agreed to roll back a proposal that would force banks to own a piece of mortgage-backed securities that they sell to institutional investors.

Senators voted to give banks a way to avoid the requirement that they hold at least a 5 percent interest in mortgages they assemble for sale. Banks lobbied against the requirement — part of a package of new financial rules the Senate is considering to ward off a repeat of the financial crisis.

The changes would permit banks to escape the 5 percent risk standard if regulators determine the residential or commercial mortgages they sell meet stringent underwriting standards.

The initial requirement was designed to force banks to have "skin in the game" and ensure that they make better loans. Toxic securities backed by bad mortgages were at the center of the 2008 economic breakdown.