By Douwe Miedema

WASHINGTON, Sept 23 (Reuters) - The U.S. swaps regulator should revise its policy that determines how its rules apply overseas, a new commissioner said on Tuesday, wading into a row between international regulators and his own agency.

Rather than sticking to its so-called cross-border guidance, the Commodity Futures Trading Commission should start a more formal rule-making process and take in industry comments, Commissioner Chris Giancarlo said.

"I believe my agency, the CFTC, started the current rift in cross-Atlantic swaps cooperation with its ... guidance," Giancarlo, currently the only Republican on a four-strong commission, said in a speech.

Swaps, a form of derivatives contract, saw their use soar prior to the 2007-2009 financial crisis when they were only lightly regulated, with trading dominated by banks such as JP Morgan Chase, Bank of America and Citigroup Inc. .

The cross-border application of the CFTC's rules is the source of a long-running dispute with the European Union, which wants the U.S. regulator to rely more on EU oversight for European companies working in America, and U.S. banks operating in Europe.

It was the first time that Giancarlo, who long worked at swaps broker GFI, gave a comprehensive oversight of his views after joining the CFTC in June. Conflicting views among the agency's political appointees are common.

"I intend to do everything I can to encourage the CFTC to replace its cross-border (guidance) with a formal rulemaking that recognizes ... competent non-U.S. regulatory regimes," Giancarlo said at a conference in Switzerland.

Last week, a U.S. court largely rejected an attempt to throw out the cross-border policy by banking groups, who had also argued that the agency had dodged a formal rule-making process by adopting the guidance instead.

Banks and other critics often blamed Gary Gensler, the CFTC's previous chairman, for his aggressive implemenation of dozens of new rules stemming from the Dodd-Frank law to reform Wall Street after the 2007-09 financial crisis.

Tim Massad, who succeeded Gensler this year, has shown signs he is a more cautious operator. He said last week that the CFTC might adopt formal rules on how to apply one particular area of the agency's policy - on margin for uncleared swaps - so as not to depend on the guidance.

(Reporting by Douwe Miedema)