(Reuters) - The United States intends to invite Iran to an international conference on Afghanistan later this month, the first overture from the Obama administration toward Tehran.

WHY IS THE UNITED STATES REACHING OUT TO IRAN?

The United States and Iran have been at odds since the 1979 Islamic revolution toppled the U.S.-backed shah.

Top of U.S. worries about Iran is the suspicion Tehran is using its nuclear energy program as a cover for building an atomic bomb. Washington is also concerned by Tehran’s backing for radical Islamist groups such as Hezbollah and Hamas.

But the United States and Iran share common interests in Afghanistan and if they first work on issues where they might be able to agree, they can then build up trust to move on to thornier problems such as the nuclear dispute.

WHAT DO THE TWO SIDES HAVE IN COMMON ON AFGHANISTAN?

The United States and Shi’ite Iran share a common dislike for the hardline Sunni Taliban.

Iran nearly went to war with Taliban-ruled Afghanistan in 1998 and Tehran armed Afghan Northern Alliance factions against the austere Islamist movement. Neither Iran nor the United States want to see the Taliban back in power again.

The United States and Iran also want to see an end to opium and heroin production in Afghanistan; Washington because it helps fund the Taliban and Tehran because the drugs are smuggled across the border and feed the habits of up to 2 million Iranians.

More than 3,500 Iranian security personnel have been killed fighting drug smugglers since Iran’s 1979 Islamic revolution.

Both sides have an interest in ensuring a stable Afghanistan.

Trade between Iran and Afghanistan is booming along an Iranian-built road to the western Afghan city of Herat. Afghanistan has just opened an Indian-built road from the Iranian border linking the main Afghan highway to Iranian ports.

More trade will help Iran but can also bring more prosperity to help stabilize Afghanistan.

WHAT ARE THE STICKING POINTS?

U.S. military commanders say Iranian-made weaponry, including sophisticated roadside bombs, have been found in Afghanistan. But no evidence has yet been uncovered to prove Iran’s government has itself provided the arms to insurgents fighting NATO-led forces and the pro-Western Kabul-government.

Analysts say Tehran does not want to see the hardline Taliban return to power, but might drip feed the insurgents in order to keep U.S. forces tied down and incapable of attacking Iran.

If Tehran is behind some weapons shipments, an atmosphere of greater trust between the United States and Iran would help cut some arms and bomb-making technology to the Taliban.

But Iran’s government would want concrete guarantees that U.S. forces will not use bases in Afghanistan to attack Iran.

While Iran’s ruling Shi’ite clerics might not want the Sunni Taliban to succeed in Afghanistan, they might also be reluctant to see a stable democracy emerge across their eastern border.