Amr El-Kahky, Al Jazeera's correspondent in Cairo, said: "We're told the [former] hostages are safe and sound and that half of the kidnappers, according to the [Egyptian] denfence minister, have been 'liqidated'."
On Sunday, Mahjoub Fadl Badri, a Sudanese presidential adviser, said that Sudanese troops had pursued the kidnappers and killed them in a gun battle.
A Sudanese soldier was also injured in the clash.
Earlier an official had said the 19 hostages, who were snatched at gunpoint during a desert safari on September 19, were "all well" and appeared to be moving from Sudan towards Egypt.
The hostages included five Italians, five Germans, one Romanian and eight Egyptians.
An Egyptian security official was reported as saying that the kidnappers and German negotiators had agreed a deal but that "negotiations were still ongoing to work out details".
The kidnappers had reportedly demanded up to $15m in ransom for releasing the hostages. Egypt's state television quoted an official as saying no ransom had been paid.