WASHINGTON (Reuters) - Secretary of State Hillary Clinton said on Sunday the United States will maintain a strong security relationship with Iraq despite the scheduled pullout of all U.S. troops and warned Iran not to try to exploit the situation.

"No one should miscalculate America's resolve and commitment to helping support the Iraqi democracy," Clinton said on the NBC program "Meet the Press." "We have paid too high a price to give the Iraqis this chance. And I hope that Iran and no one else miscalculates that."

Clinton, speaking on the program "Fox News Sunday," added that Iraq "is a sovereign, independent nation with whom we have very good relations. And we expect to have a continuing strong security relationship for many years to come."

After months of negotiations with officials in Baghdad failed to reach an agreement to keep possibly thousands of U.S. troops in Iraq as trainers, U.S. President Barack Obama announced on Friday he would stick to plans to pull out the remaining force of 40,000 American troops by year's end.

The announcement was a milestone more than 8 1/2 years after the Bush administration led the invasion to topple Saddam Hussein based on warnings of weapons of mass destruction that turned out not to exist.

"What we've agreed to is a support and training mission similar to what we have in countries from Jordan to Colombia. And we will be working with the Iraqis. We will also have a very robust diplomatic presence," Clinton said.

Iran already is at odds with Washington and other Western governments over its nuclear ambitions and Clinton warned Tehran against trying to exert its influence in neighboring Iraq.

"Iran would be badly miscalculating if they did not look at the entire region and all of our presence in many countries in the region," she said on the CNN program "State of the Union" from Uzbekistan.

(Reporting by Will Dunham; Editing by Bill Trott)