By Matt Spetalnick

WASHINGTON, Aug 9 (Reuters) - U.S. President George W. Bush insisted on Thursday that Iran is a destabilizing force in Iraq despite Tehran's assertion to Iraqi Prime Minister Nuri al-Maliki that it is helping secure his country.

Calling Iran a "very troubling nation" that should be isolated, Bush warned during a White House news conference: "When we catch you playing a nonconstructive role (in Iraq), there will be a price to pay."

Bush spoke as Maliki, facing deepening political woes at home and U.S. criticism for lack of progress in bridging sectarian divisions, won pledges of support from Shi'ite Iran during a visit to the neighboring country.

Playing down signs of warming ties between Baghdad and Tehran, Bush -- struggling to rally U.S. public support for the unpopular Iraq war -- voiced confidence that he and Maliki see eye-to-eye on Iran as a threat to Iraqi security.

"If the signal (from Maliki) is that Iran is constructive, I will have to have a heart-to-heart with my friend, the prime minister. Because I don't believe they are constructive," Bush said. "I don't think he, in his heart of heart, think they're constructive either."

It was the second time this week that Bush has had to defend his tough stance on Iran in the face of possible differences with a key ally.

He warned Afghan President Hamid Karzai on Monday during a visit to the U.S. presidential retreat at Camp David to be more suspicious of Iran after the Afghan leader had brushed aside U.S. accusations that Tehran was arming the Taliban.

Iran, with a majority of Shi'ite Muslims like Iraq, has been an important political player in Iraq since the 2003 U.S.-led invasion.

Tehran denies Washington's accusations that it is supplying weapons to militants to stoke violence, and instead blames the U.S. military presence. Baghdad has urged both countries to negotiate and not fight out their differences on Iraqi soil.

IRAN PLEDGES SUPPORT TO MALIKI

During Maliki's visit, Iran's First Vice President Parviz Davoudi told him Tehran "has always made a special effort to help provide and strengthen security in Iraq," the official IRNA news agency reported.

But Bush dismissed the idea that Iran was playing a positive role in Iraq, where violence between majority Shi'ites and minority Sunnis has seemed at times to verge on civil war.

That has contributed to growing demands from Democrats who control the U.S. Congress for a timetable for U.S. withdrawal, something Bush has rejected.

Bush said Maliki "knows that weaponry being smuggled in to Iraq from Iran and placed into the hands of extremists -- over which the government has no control, all aimed at killing innocent life -- is a destabilizing factor."

He reiterated Western accusations that Iran's uranium enrichment program is aimed at creating nuclear weapons, saying, "That in itself, coupled with their stated foreign policy, is very dangerous for world stability."

Tehran insists its nuclear program is solely aimed at producing electricity.

The U.N. Security Council has imposed two rounds of sanctions since December on Iran for failing to halt uranium enrichment. A third sanctions resolution is being considered. (Additional reporting by Jeremy Pelofsky)

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