The report could not be confirmed, although journalists who visited the region on Sunday said that thousands of Eritrean troops had taken up defensive positions.
In December 2007, an estimated 4000 Eritrean troops remained in the 'demilitarized zone' with a further 120,000 along its side of the border.
The Ethiopians claimed to have killed 3,000 Eritrean troops during the Christmas offensive.
In 1998 Eritrean troops occupied Badme, which it claimed and Ethiopia held.
Ethiopia said Eritrean troops fled after fighting around the town, which Ethiopia claims.
In a statement released tonight, Ethiopia said it had captured several more "strategic" towns, along with Eritrean troops and equipment.
And the officials stopped along a roadside lined with perhaps 15 corpses, bloated in the baking sun, that they said were Eritrean troops.
The Foreign Ministry said Eritrean troops would withdraw to positions held before the war started.
About halfway through the battle, over nine hundred of his Eritrean troops deserted.
He said Eritrean troops were forced to fortify new lines of defense three days after Ethiopia began an offensive.