By Lisa Lambert and David Lawder

WASHINGTON (Reuters) - Dialing back the Volcker Rule that limits banks' ability to engage in speculative investments is a top priority for President Donald Trump's nominee for U.S. Treasury secretary, Steve Mnuchin, according to a document seen by Reuters on Monday.

In written responses to questions posed by members of the U.S. Senate Finance Committee, Mnuchin said he would use his role as head of the interagency Financial Stability Oversight Council to give the Volcker Rule a stricter definition of proprietary trading.

In "prop trading" a financial firm uses its own money to invest in privately held companies, hedge funds and similar vehicles. The Volcker rule was designed to limit the type of risk-taking activities that helped land banks in trouble during the financial crisis.

"As Chair of FSOC I would plan to address the issue of the definition of the Volcker Rule to make sure that banks can provide the necessary liquidity for customer markets and address the issues in the Fed report," Mnuchin wrote in the document, which also included senators' questions and was verified by a Senate aide.

During his confirmation hearing with the Senate Finance Committee last week, Mnuchin cited a recent Federal Reserve report that found the rule, part of the 2010 Dodd-Frank Wall Street Reform law, was limiting market liquidity. The committee has not yet scheduled a date to vote to send the nomination to the full chamber for approval.

Regulators have applied proprietary trading prohibitions to too many activities, he said.

The Fed report found that ambiguity and gray areas in the rule were pushing dealers to conservative strategies to ensure they did not cross the line on the prohibitions.

In the responses Mnuchin also made it clear he believes the rule should only apply to "a bank that benefits from federal deposit insurance." The Federal Deposit Insurance Corporation guarantees retail deposits at about 6,000 banks, including the consumer banking arms of the country's largest investment banks.

The law currently applies to banks that have access to the Federal Reserve's discount window or other government backstop.

Senator Maria Cantwell, a Democrat who serves on the Finance Committee, wrote that uninsured investment banks also pose risks that the rule, named for former Federal Reserve Chair Paul Volcker, was supposed to address.

"As we saw during the financial crisis, when nonbanking affiliates of FDIC insured banks failed, they were rescued by their insured affiliates, which in turn were forced to be rescued by taxpayers," she wrote. "This was the case with State Street Bank, and your former employer, Goldman Sachs, which converted to a bank holding company in order to be eligible for federal bailout funds."

Mnuchin reiterated that an updated version of the 1933 Glass-Steagall law that had long separated commercial and investment banking should be instated to reduce risks. The law was repealed in 1999.

Mnuchin has not shared details of his "21st Century Glass-Steagall," but hinted it would be looser than the original.

"A bright line between commercial and investment banking, although less complicated, may inhibit the necessary lending and capital markets activities to support a robust economy," he wrote.

(Reporting by Lisa Lambert; Editing by Linda Stern and Leslie Adler)