WASHINGTON, Sept 1 (Reuters) - In a setback for gun dealers in four U.S. states bordering Mexico, a federal judge on Thursday refused to temporarily block new rules requiring them to report the sale of multiple semi-automatic rifles.

Judge Rosemary Collyer said the dealers, backed by the National Rifle Association, had not sufficiently shown they would suffer irreparable harm without a preliminary injunction. She scheduled an October hearing on a permanent injunction.

The Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) ordered more than 8,000 gun dealers in Texas, Arizona, New Mexico and California to report the sale within five business days of two or more rifles to the same person.

The Obama administration issued the reporting requirements to try to stem the flow of weapons across the border to violent drug cartels in Mexico. Mexican officials have complained bitterly about guns illegally coming from the United States.

The gun industry says the rules will not affect the cartels' efforts but rather burden law-abiding retailers.

Two gun dealers backed by the NRA, one of the most powerful lobbying groups in the United States, and the National Shooting Sports Foundation sued to block the rules arguing that the ATF was not authorized to require such reporting and the reports were unfairly burdensome.

"I'm very skeptical if there is irreparable harm," Collyer told lawyers for the gun dealers after they had said their clients had to set up costly new systems and that there were more costs to regularly produce the information for the ATF.

Collyer instead set an aggressive schedule for resolving the matter, ordering oral arguments on Oct. 25 on whether a permanent injunction to block the rules was warranted. Whatever decision she makes will likely be appealed.

The gun industry also has filed similar challenges in New Mexico and Texas. The Obama administration has sought to have the cases consolidated into the case in Washington, D.C.

The case is National Shooting Sports Foundation Inc et al v. Melson, U.S. District Court, District of Columbia, No. 1:11-cv-1401.

For the National Shooting Sports Foundation: Andrew Lothson and James Vogts of Swanson, Martin & Bell; Vincent Verrocchio of Venable.

For J&G Sales and Foothills Firearms: Richard Gardiner; Stephen Halbrook.

For Melson: Daniel Riess, Lesley Farby and Jessica Leinwand of the Justice Department.

(Reporting by Jeremy Pelofsky)

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