By Randall Mikkelsen

WASHINGTON, April 13 (Reuters) - Iraq is prepared to pressure Iran diplomatically to stop supporting violence, while the United States helps the military effort to halt aid to "surrogate" forces, the White House national security adviser said on Sunday.

However, U.S. Defense Secretary Robert Gates said chances of a violent confrontation with Iran were slim.

White House adviser Stephen Hadley said Iran must choose between good relations with Iraq, or its "destabilizing" activities in the country.

"The Iraqi government now understands more clearly what they (the Iranians) are doing. They will put diplomatic pressure to bear on Iran. That's a good thing," Hadley said on the "Fox News Sunday" television show.

"In addition, we will continue to do with Iraqi security forces what we've been doing for some time. We will go after their surrogate operations in Iraq that are killing our forces, killing Iraqi forces.

"We will disrupt their networks by which they move fighters, weapons and funds in and around Iraq. And we will cut off as best we can the flow of fighters, weapons and arms into Iraq," he said.

Washington accuses Iran of stoking violence in its neighbor. Iran denies this and blames the presence of U.S. troops for the bloodshed.

Iraqi Foreign Minister Hoshiyar Zebari described Iran as a neighbor that must be treated with respect.

"We are destined to live with them. Really, we need to assume some good faith in dealing with them, trying to ... activate this tripartite dialogue between the United States, Iran and Iraq," Zebari said on CNN's "Late Edition."

Gates, speaking on CBS's "Face the Nation," said Iraqi forces were steadily assuming control of more areas in Iraq, and he cited reports of a backlash among some local Shi'ite leaders in Basra against violent Shi'ite factions.

"I think the chances of us stumbling into a confrontation with Iran are very low. We are concerned about their activities in the south," he said. "But I think that the process that's under way is ... headed in the right direction."

House of Representatives Speaker Nancy Pelosi, a California Democrat, called the Iraqi government the main obstacle to ending factional and sectarian violence, and said on "Face the Nation" that an early withdrawal of U.S. troops would force the government to make political decisions needed for peace.

(Editing by Eric Beech)

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