WASHINGTON, April 10 (Reuters) - U.S. President George W. Bush issued a stark warning to Iran to stop interfering in Iraq on Thursday and characterized Iran and al Qaeda as "two of the greatest threats to America."

In a speech at the White House, Bush, who has accused Iran of backing militant groups in southern Iraq and providing explosives to extremists in the country, said Tehran had a choice in its relations with Iraq.

"(It) can live in peace with its neighbor, enjoy strong economic and cultural and religious ties, or it can continue to arm and train and fund illegal militant groups which are terrorizing the Iraqi people and turning them against Iran," Bush said.

"If Iran makes the right choice, America will encourage a peaceful relationship between Iran and Iraq. If Iran makes the wrong choice, America will act to protect our interests and our troops and our Iraqi partners."

Iran's leaders have developed strong links with fellow Shi'ite leaders in Baghdad, who assumed power after the 2003 U.S.-led invasion ousted the government of Sunni President Saddam Hussein.

The two countries fought a costly war in the 1980s when Saddam was in power.

Bush said Iraq was "the convergence point for two of the greatest threats to America in this new century: Al Qaeda and Iran."

"If we fail there, al Qaeda would claim a propaganda victory of colossal proportions and they could gain safe havens in Iraq from which to attack the United States, our friends and our allies," the president said.

"Iran would work to fill the vacuum in Iraq. And our failure would embolden its radical leaders and fuel their ambitions to dominate the region."

During hearings in Congress on Iraq this week, some Democrats expressed dismay at the close relations between the rulers in Baghdad and Tehran's Islamic leaders.

They noted Iranian President Mahmoud Ahmadinejad was given a warm public reception when he visited Baghdad, while visits by Bush and other U.S. leaders have been unannounced in advance and cloaked in tight security.

Relations between Washington and Tehran have been hostile since the Islamic takeover in 1979, when U.S. diplomats were held hostage. The United States is leading international efforts to rein in Iran's nuclear program, which it says is aimed at making weapons. (Reporting by David Storey; Editing by Bill Trott)

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