One Iraqi official said that Iraqi soldiers in two vehicles had intercepted a car carrying Sharafi at 6pm on Sunday in a predominantly Shia area.
Alireza Ranaghi, Al Jazeera's correspondent in Iran, said the interior ministry did not deny or confirm that the four men had admitted that there were following American orders.
Tony Snow, a White House spokesman, said on Tuesday: "All we know is that the Iraqi government is investigating it and obviously we abide by and support the Vienna convention for the diplomats, but we don't really know a lot about it at this point."
Mohammad Ali Hosseini, an Iranian foreign ministry spokesman, said Sharafi was seized by a group working under US supervision.
He said: "Based on reliable information, the group which has committed this completely terrorist act, are active under the supervision of the American forces.
"The Islamic Republic of Iran strongly condemns this aggressive act which is in violation of international law."
Lieutenant Colonel Christopher Garver, a US military spokesman in Baghdad, said that no US troops, or Iraqi troops that report to them, were involved in the incident.
"We've checked with our units and it was not an MNF-I [multinational forces – Iraq] unit that participated in that event," Garver said, referring to a special Iraqi force that is directed by the US military.
Iran and the US broke off diplomatic relations in 1980.
Iran on Tuesday summoned the ambassadors of Iraq and Switzerland, which represents US interests in the Islamic republic.
Philippe Welti, the Swiss ambassador to Iran, and Mohammed Majid al-Sheikh, the Iraqi ambassador, were summoned to meetings with their respective regional directors at the foreign ministry.
The Iranian foreign ministry told the envoys: "The kidnapping was contrary to international laws and the diplomat should be released at once and those who committed the terrorist act punished."
Iraqi and Iranian officials said that Sharafi was seized by 30 gunmen wearing Iraqi army uniforms as he drove through a central Baghdad neighbourhood.
The Iraqi soldiers took Sharafi to another car and sped away.
Iraqi police officers suspected that a kidnapping was taking place and opened fire on the cars, and detained some of the occupants.
Those who were detained were released on Monday.
The Iraqi troops were part of an army unit that receives direct orders from the US military, the Iraqi official said, declining to be identified because of the sensitivity of the information.
The White House has authorised US troops in Iraq to kill or capture Iranian agents deemed to be a threat, saying evidence was mounting that Iran was supporting "terrorists" inside Iraq.
The US has accused Iran of being a major supplier of bombs and other weapons used to target US forces. Tehran has denied the charges.
Tensions have flared between the US and Iran over US-led efforts to isolate Iran and force it to abandon its suspected nuclear weapons programme.
Source: Al Jazeera and agencies