"Today, the Bashmagh border crossing was reopened," its director Jahangir Bakhshi told state broadcaster IRIB.
"No decision has been taken by authorities regarding the Haji Omran and Parvizkhan border posts," he added.
The Bashmagh crossing lies on the road to the city of Sulaimaniyah in the south of the autonomous region, a bastion of opposition to Iraqi Kurdish leader Massud Barzani, who called the September 25 independence referendum.
The vote antagonised not only Baghdad but also neighbouring Iran and Turkey, which are fearful of anything that might stoke separatist sentiment among their own large Kurdish minorities.
On October 15, Baghdad announced that Tehran had agreed to close its land border with Iraqi Kurdistan too.
Baghdad has also sent in troops and allied militia to wrest back control of swathes of disputed territory long claimed by the Kurds, leaving the autonomous Kurdish region's finances in disarray.
Today, Iraqi Kurdish leaders offered to freeze the outcome of last month's vote, taking a step back in the crisis. There was was no immediate response from Baghdad.
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