"The land border between Iran and the Kurdistan region of Iraq is open," the ministry said in a statement.
"For now, only air borders between Iran and this region are closed," it added.
The latest statement corrects an earlier one given by foreign ministry spokesman Bahram Ghasemi.
"At the request of the Iraqi government, we have closed our land and air borders," he said.
It followed reports on Sunday evening that Tehran had ordered all flights to and from Iraqi Kurdistan to be halted in response to the independence referendum.
Iran has a large Kurdish minority around its Iraqi border, some of whom have called for independence.
Tehran is also a firm backer of the Iraqi government and the Hashd al-Shabi militia alliance, which has been positioned around territories disputed by Baghdad and Erbil.
The New ArabComments