* Fattal, Bauer set for July 31 hearing
* Pair were arrested in 2009 by Iranian forces
By Megan Davies
NEW YORK, July 2 (Reuters) - Iran denied in a statement issued by its U.N. mission on Friday that two U.S. citizens detained on spying charges have been mistreated, saying they had consular contact and a visit from their families.
Josh Fattal and Shane Bauer, together with Bauer's fiancee Sarah Shourd, were arrested by Iranian forces on July 31, 2009, on suspicion of spying after crossing into Iran from neighboring Iraq.
Shourd, who was released on bail in September and returned home, has insisted the trio were innocent hikers who unintentionally crossed the unmarked border into Iran.
The families said in a letter released on Thursday that Fattal and Bauer had been subjected to psychological torture as a result of extreme isolation, had been denied access to their lawyer and to consular visits from Swiss diplomats who represent U.S. interests in Iran.
The letter, addressed to Ahmed Shaheed, the United Nations human rights investigator on Iran, also claimed Fattal and Bauer were assaulted and sexually harassed by a prison guard.
"Two years later, Shane and Josh are still in prison in deplorable conditions," Shourd said at a press briefing at the United Nations earlier in the week.
Iran's mission to the United Nations called these "baseless allegations" in a press statement released late on Friday.
"We categorically deny Ms Shourd's recent false claims and the repeat of the same allegations by some family members, about the treatment of the two U.S. citizens by Iranian authorities," the statement said.
The families said they met with U.N. Secretary General Ban Ki-moon earlier in the week and said in a press release on Thursday that Ban had called Bauer and Fattal's imprisonment "totally unacceptable." A U.N. spokesman could not immediately vouch for the accuracy of the quote.
Iran's statement also alleged there are Iranian citizens "imprisoned in the U.S. under false and unproven accusations." It called on the United Nations to "play an effective role" in clarifying "the fate of ... imprisoned Iranians in the U.S."
Bauer and Fattal pleaded not guilty at a closed-door court hearing on Feb. 6. Iran is scheduled to hear the case against them on July 31. Under Iran's Islamic law, espionage can be punished by execution.
Iran's statement said "any attempt to politicize the matter beyond its legal nature would be harmful and useless".
The case has further complicated relations between Tehran and Washington already fraught over Iran's nuclear activity.
The U.S. State Department in June renewed its call on Iran, with which Washington has no diplomatic ties, to release the two men.
Western powers suspect Iran is trying to develop nuclear weapons under the cover of an atomic energy program. Tehran denies this, saying its nuclear activity is entirely peaceful. (Editing by Todd Eastham)