OTTAWA (Reuters) - Canada stepped up pressure on Washington on Monday to rewrite its controversial Volcker rule to remove restrictions on Canadian bank activities that it says do not threaten the U.S. financial system.

Bank of Canada Governor Mark Carney, who is also chairman of the Financial Stability Board, a global watchdog set up by the Group of 20 nations, and Finance Minister Jim Flaherty laid out their complaints about the rule, included in the 2010 Dodd-Frank financial oversight law, in letters to their U.S. counterparts.

Canada’s banks are so interconnected with U.S. financial system that the law’s ban on proprietary trading would rob the Canadian government bond market of needed liquidity and hamper bank-sponsored hedge funds unnecessarily, they argued.

The draft rule targets activities that actually help strengthen Canada’s financial system, they said.

“The Volcker rule as drafted would also potentially apply to Canadian banks’ much larger Canadian operations, which pose no risk to U.S. taxpayers or U.S. financial stability,” Flaherty wrote in his letter to U.S. Treasury Secretary Timothy Geithner.

“The Volcker rule could apply to transactions between Canadian banks that are simply facilitated by U.S.-based financial infrastructure, such as U.S. clearing houses. This could have unintended adverse consequences for the U.S. financial system,” he wrote.

The rule prohibits banks that receive government backstops such as deposit insurance from making risky trades with their own funds.

It makes an exception for U.S. Treasuries. Canada has been one of the most outspoken countries requesting that the exemption be extended to their own government debt markets.

Their arguments have not moved the rule’s namesake and champion, former U.S. Federal Reserve Chairman Paul Volcker, who last month dismissed Canada’s concerns as unimportant and said the country did not rely on the United States for proprietary trading.

Carney proposed two amendments to the draft rule on behalf of Canada in his letter to Federal Reserve Chairman Ben Bernanke.

One change would address a concern that Canadian banks would face restrictions for market-making and hedging activities even if they pose no risk to the U.S. financial system.

The draft rule treats Canadian mutual funds on par with U.S. hedge funds and private equity funds, which could prevent some banks from sponsoring mutual funds that deal with U.S. residents for fear of non-compliance.

“The difficulty of distinguishing legitimate market-making activities from prohibited proprietary trading could reduce trading activity and could severely disrupt the liquidity and resilience of Canadian financial markets,” Carney wrote.

Secondly, he suggests that Canadian government securities be exempt from the ban on proprietary trading.

Carney’s concerns extend beyond Canada. He said the rule appears to prevent non-U.S. banks from entering transactions that may involve U.S.-based market infrastructure such as trading platforms and clearing houses.

This could make it difficult to carry out global financial reforms that call for increased use of trading platforms and central clearing for derivatives, he said.