FACTBOX: Ups and downs in U.S.-Iranian relations

(Reuters) - The new U.S. administration needs to show a "fundamental" change in policy not just tactics, Iran's president said on Wednesday after U.S. President Barack Obama offered to extend a hand of peace to the Islamic Republic.

Unpicking decades of confrontation and mutual hostility will be no easy task - here are some details of turbulent relations between Iran and the United States.

* 1953 - A COUP:

-- In August 1953, the CIA helped orchestrate the overthrow of Iran's popular prime minister, Mohammed Mossadegh, restoring the Shah, Mohammed Reza Pahlavi, to power.

-- Washington acted after Britain, opposed to Mossadegh's policy of nationalizing the British-controlled oil industry, convinced U.S. officials the prime minister was turning to communism. As Britain's power faded, the United States became the symbol of what many Iranians saw as Western imperialism.

* 1972 - CEMENTING A RELATIONSHIP:

-- A 1972 visit by U.S. President Richard Nixon cemented a close strategic relationship between Iran and the United States. But opposition to the Shah, led by exiled cleric Ayatollah Ruhollah Khomeini, mounted.

* 1979 - KHOMEINI RETURNS:

-- After bloody clashes between protesters and troops, the Shah fled into exile in January 1979. The next month, Khomeini returned to Iran in triumph to seal victory for a revolution whose mantra was "Death to America."

-- In November 1979, Iranian students seized the U.S. embassy in Tehran and took 90 hostages; 52 were held captive for 444 days, prompting Washington to break relations in 1980.

* 1986 - AN ARMS DEAL

-- U.S. President Ronald Reagan admitted to secret arms deals with Iran that broke a U.S. embargo. The trade was aimed at winning the release of Americans held by pro-Iranian Shi'ite militants in Lebanon. Money from the sales was secretly passed to U.S.-backed Contra guerrillas in Nicaragua. At the time, Iran was embroiled in war with President Saddam Hussein's Iraq, in which the United States gave increasing support to Baghdad.

* 1997 - REFORMISTS IN CHARGE:

-- Iranian voters swept reform-minded President Mohammad Khatami to power. He promoted a "dialogue among civilizations." During his term, Iranians staged an impromptu vigil in Tehran when hijacked planes struck U.S. targets on September 11, 2001.

-- After those al Qaeda attacks, Iran offered support in a U.S.-led war to topple Afghanistan's Taliban leaders shielding al Qaeda chief Osama bin Laden. Iran helped ensure the success of a multilateral postwar conference on Afghanistan's future. In January 2002, U.S. President George W. Bush branded Iran part of an "axis of evil" and accused it of seeking nuclear weapons.

* 2003 - INVASION OF IRAQ:

-- The U.S.-led invasion of Iraq removed Saddam, a Sunni Arab leader who had been a deadly enemy of Iran, and brought to power Iraqi Shi'ite factions with closer links to Tehran.

-- As Iraq descended into insurgency and sectarian conflict, the United States accused Tehran of arming, funding and training Shi'ite militias that have attacked U.S. forces in Iraq. Iran denied this, blaming the U.S. troop presence for the violence.

* 2008 - A NUCLEAR ROW:

-- The United States led efforts to toughen U.N. sanctions on Iran over its nuclear program and in March the Security Council adopted a third sanctions resolution. Iran says the program is lawful, peaceful and designed only to generate electricity, but it has failed to convince the West.

-- U.S.-Iran tensions have worsened since the 2005 election of President Mahmoud Ahmadinejad, who has berated the West, queried the Holocaust and called for Israel to be wiped off the map. In a surprise development, a U.S. National Intelligence Estimate in late 2007 said Iran had put nuclear military plans on hold in 2003.

2009 - A NEW ADMINISTRATION:

-- New U.S. President Barack Obama said this week America was prepared to extend a hand of peace to Iran if it "unclenched its fist." Ahmadinejad welcomed change in response but on condition that the change is fundamental and on the right track.