An Iraqi official played down the incident, saying the area was abandoned and right on a disputed border section.
Iranian soldiers crossed the border and raised an Iranian flag over the Fakkah oil field, a US military spokesman told the AFP news agency.
But an Iranian oil company spokesman denied the accusation, saying no troops had taken control of any oil well.
"The company denies Iranian soldiers taking control of any oil well inside Iraqi territory," the National Iranian Oil Company spokesman was quoted as saying by Iranian media.
Iraq's Deputy Interior Minister confirmed the Iranians stayed in Iraq and were in control of the well.
We are awaiting orders from our leader
Ahmed Ali al-Khafaji
Deputy Interior Minister
Earlier it was reported that they had withdrawn back across the border.
Deputy Interior Minister Ahmed Ali al-Khafaji initially told the Reuters news agency the reports of the Iranian incursion were not true.
But Mr Khafaji later confirmed the incursion had taken place, and said 11 Iranians had dug-in at the oil well and had not left.
"At 3:30 this afternoon, 11 Iranian soldiers infiltrated the Iran-Iraq border and took control of the oil well. They raised the Iranian flag, and they are still there until this moment," he told the Reuters news agency.
He said there had been no military response from Iraqi forces.
"We are awaiting orders from our leader," he said.
The incursion is one of several that have occurred in the last few days, he said.
The well is about 500m from an Iranian border fort and about 1km from an Iraqi fort, US Colonel Peter Newell told AFP.
Edited to bold some stuff.