Iran's nuclear programme, which Washington believes to be a bid for developing atomic weapons, is not scheduled to be discussed.
The talks come two days after Tehran said it had uncovered Western spy networks on its territory and a flotilla of US Navy warships commenced war games in the Gulf.
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.
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.
"Iran has a right to pursue nuclear power but it should abide by international agreements and laws"
David, NYC, US
Send us your views
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Chatham House think-tank says the Islamic state, which has close ties to fellow Shia in Baghdad's government, has superseded the US as the most influential power in Iraq.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 troops.
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.