Iran's nuclear programme, which Washington believes to be a bid for developing atomic weapons, is not scheduled to be discussed.
Anthony Cordesman, a Middle East expert at Washington's Centre for Strategic and International Studies, cautioned against expecting too much from the talks. "One needs to be very careful about confusing progress with dialogue," he said.
"The US knows what it wants from Iran ... but it is far from clear that it can get it. The US wants Iran to stop support for Shia militias and providing arms. At the same time the administration cannot offer much in return," he said.
"Iran has a right to pursue nuclear power but it should abide by international agreements and laws"
David, NYC, US
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Crocker has said he does not expect "any stunning, startling breakthroughs" from the meeting. US officials say he will press Iran to take steps to reduce violence in Iraq.
In the past few months, the US military has displayed explosively formed penetrators (EFPs) - roadside bombs - and other weapons which it says are being supplied by Iran to Iraqi fighters in order to target US soldiers.
Iran denies it is fomenting violence and has called on US forces to get out of Iraq, saying their presence is fuelling sectarian violence.
The US military also claims Shia fighters are receiving funding and training in Iran.
In February, US troops detained five Iranians accused of ties to Iran's Revolutionary Guards, which angered Iran who insist they are diplomats.
Manouchehr Mottaki, Iran's foreign minister, said last week he had been assured by Zebari they could be released by June 21.
A report on Iran by the influential Chatham House think-tank says the Islamic state, which has close ties to fellow Shia in Baghdad's government, has superseded the US as the most influential power in Iraq.
George Bush, the US president, who initially rejected talks with Iran, has come under mounting domestic pressure to end the war and pullout some 150,000 US soldiers.
Despite the 27-year freeze in formal ties, mid-ranking officials from the two countries have met occasionally, most recently to discuss Afghanistan prior to and following the US-led war to overthrow the Taliban.
Iran's intelligence ministry has meanwhile claimed to have broken up spy networks led by coalition forces in Iraq.
"The espionage activities of the United States government on the soil of the Islamic Republic of Iran are in contradiction to international treaties"
Ahmad Sobhani, Iranian foreign ministry spokesman for the Americas
"The espionage activities of the United States government on the soil of the Islamic Republic of Iran are in contradiction to international treaties," said Ahmad Sobhani, the Iranian foreign ministry spokesman for the Americas.
"Spy networks, guided by American intelligence services, have recently been discovered in west, southwest and central Iran," said Sobhani.
On Sunday, Iran's foreign ministry summoned the Swiss ambassador to Tehran to condemn the alleged spying.
The Swiss embassy represents US interests in Iran, because Washington has not had a mission there since 1980.