Legislation that would write into law and widen the proposed "Volcker rule" to limit proprietary trading was unveiled in the U.S. Senate on Wednesday with the support of five Democratic senators.

The bill, drawn up by senators Jeff Merkley and Carl Levin, would apply not only to banks, but also to "large, interconnected nonbank financial institutions," said a summary of the measure from Merkley's office.

He and Levin were joined in backing the bill by Democratic senators Ted Kaufman, Sherrod Brown and Jeanne Shaheen.

The "Volcker rule" idea was first put forward in January by President Barack Obama and White House economic adviser Paul Volcker. As proposed, it would ban banks which enjoy federal insurance protection from buying and selling investments for their accounts unrelated to customers' needs.