(Corrects name of American Academy of Diplomacy in sixth paragraph)

WASHINGTON, May 14 (Reuters) - U.S. Defense Secretary Robert Gates called on Wednesday for more unofficial contacts with Iran, saying this might eventually open a pathway to more substantive dialogue between the governments.

The United States, which cut diplomatic ties with Iran after its 1979 Islamic revolution, accuses Iran of fomenting violence against U.S. troops in Iraq and of pursuing nuclear weapons.

Iran denies both accusations, saying Washington is ultimately responsible for the violence in Iraq following the U.S.-led March 2003 invasion and that its nuclear program is solely to generate electricity.

While the two countries have had talks on defined subjects in recent years, including Afghanistan and Iraq, this has not blossomed into the broad engagement recommended by the blue-ribbon Iraq Study Group report issued in December 2006.

Gates, who has previously argued for engagement with Iran, suggested this was less likely now because of a more hard-line stance by its President Mahmoud Ahmadinejad and what he described as the "very unambiguous ... negative" role in Iraq.

"My own view, just my personal view, would be we ought to look for ways outside of government to open up the channels and get more of a flow of people back and forth," he said in a speech to the American Academy of Diplomacy, a group of retired U.S. diplomats.

"There are actually a fair number of Iranians that come to the United States to visit. We ought to increase the flow going the other way," he said. "I think that may be one opening that creates space, perhaps, over some period of time."

He also said the United States needs to find more leverage over Iran, saying a negotiation would only be possible if Washington had something to offer Tehran.

The United States has offered to talk to Iran about any subject if it first suspends its uranium enrichment work, which could provide fuel for power plants or nuclear weapons. Iran has refused to do this and has not taken up U.S. overtures, including one by U.S. Secretary of State Condoleezza Rice.

"We need to figure out a way to develop some leverage with respect to the Iranians and then sit down and talk with them," Gates said. "If there's going to be a discussion, then they need something too." (Reporting by Arshad Mohammed; editing by Cynthia Osterman and Frances Kerry)

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