Khartoum seized Abyei on May 21, setting off an international outcry and stoking fears the two sides could return to full-blown conflict. Tens of thousands of people fled the fighting.
The proposals announced late on Tuesday said northern armed forces should remain north of the Bahar al-Arab river and the southern army should remain south, "without participating in any administrative tasks until a final solution is reached through a referendum".
The south is scheduled to secede on July 9, after it voted overwhelmingly for independence in a January referendum promised by a 2005 peace deal that ended decades of civil war.
A separate referendum was scheduled for Abyei to determine its status but that vote has not happened yet.
Under the north's proposals, Abyei's administration would be transferred to a joint committee on July 8, a statement carried by the state news agency SUNA said.
International peacekeepers in the region would be replaced by troops "of African nature," it added.
There was no immediate reaction to the proposals from southern officials, who have called on the north to withdraw from Abyei.
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