But Iran has denied that it had violated Iraq's sovereignty.
Iran's Armed Forces Command issued a statement on Saturday making clear that, in Tehran's view, there had been no incursion into Iraq as the oil well is within Iranian borders.
"Our forces are on our own soil and, based on the known international borders, this well belongs to Iran," the statement said.
Well 4 is in the al-Fauqa Field, part of a cluster of oilfields which Iraq unsuccessfully put up for auction to oil majors in June. The field has estimated reserves of 1.55 million barrels.
Ramin Mehmanparast, an Iranian foreign ministry spokesman, accused "external sources in Iraq" of working to damage relations between the governments in Tehran and Baghdad, the official IRNA news agency reported.
And a senior Iranian MP also tried to play down the dispute.
"The claim that Iran has occupied an Iraqi oil well is strongly rejected," Alaeddin Borujerdi, head of parliament's national security and foreign policy commission, told IRNA.
The issue was "being examined through diplomatic channels," he said, blaming "foreign media for such propaganda."
But Muhammad al-Hajj Hamud, Iraq's deputy foreign minister, rejected Iranian claims on the well and called for an Iranian unit made up of around a dozen soldiers and technicians to be withdrawn.
"We summoned Iran's ambassador to Baghdad [on Friday] to tell him that this attack is unacceptable and our ambassador to Tehran delivered a note to their foreign ministry to ask them to pull out their troops," he said.
Hamud said it was the first time Well 4 had been taken over.
"In the past, the Iranians would try to prevent our technicians from working on the well ... by firing in their direction," he said, adding Iraq had dug the well in 1974.
The Iraqi official said the incident comes a month before a joint commission starts work on demarcating the two countries' land and sea border along the Shatt al-Arab waterway in the south.
Admiral Michael Mullen, the chairman of the US Joint Chiefs of Staff, told reporters in Baghdad that as far as Washington was concerned "it's a sovereignty issue", adding that there were five other fields under dispute.
And in southern Iraq, a US military spokesman told AFP that the incident at Well 4 was the latest in a series of such activity along the frontier.
"The oilfield is in disputed territory between Iranian and Iraqi border forts," said the officer at Contingency Operating Base Adder, just outside the city of Nasiriyah.
The well lies about 500 metres from an Iranian border fort and about one kilometre from an Iraqi border fort, US Colonel Peter Newell said.