Iraq considers the well to be part of its al-Fauqa oil field.
Iran's armed forces, however, issued a statement on Saturday saying that, in Tehran's view, there had been no incursion into Iraq as the oil well was 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.
Foreign ministers from both countries late on Saturday discussed a "misunderstanding" between the countries' border guards.
Iraq's state-owned South Oil Company in the southeastern city of Amara said on Friday that an Iranian unit had taken control of the the well.
Baghdad demanded that Tehran pull back the soldiers who they said had "occupied" the disputed well, and condemned the incident as "a violation of Iraqi sovereignty".
The al-Fauqa field is one of several oil rich areas that Iraq unsuccessfully put up for auction to oil companies in June. The field has estimated reserves of 1.55 million barrels.
Muhammad al-Hajj Hamud, Iraq's deputy foreign minister, said it was the first time the well had been taken over during years of tension.
"In the past, the Iranians would try to prevent our technicians from working on the well ... by firing in their direction," he said, adding that Iraq had dug the well in 1974.
A joint commission is set to start work on demarcating the two countries' land and sea border along the Shatt al-Arab waterway in the south next month.
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.