A Sudanese soldier was also injured in the clash, Egypt's official MENA news agency quoted the Sudanese army as saying, adding that the hostages were now being held at a place called Tabbat Shajara, just inside Chad.
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.
Fadl named the dead alleged Darfur commander as "Bakheet", but did not say to which of the many groups in the conflict-ravaged western Sudanese region he belonged.
Mahgoub Hussein, a London-based spokesman for a key faction of the Darfur rebel Sudan Liberation Army (SLA), said: "We completely deny any report that we are involved in this kidnap.
"The movement, or any individual member, have no connection with the kidnappers, and in fact we condemn the action."
He offered a warning to those seeking the safe release of the group.
"Knowing the region and the behaviour of men like the kidnappers, we urge all parties to exercise restraint and enter in direct dialogue.
"Any attempt by force may affect directly the hostages."
An Egyptian security official told AFP that the kidnappers and German negotiators had agreed a deal but that "negotiations were still ongoing to work out details".
The kidnappers have demanded that Germany take charge of the payment of an $8.8m ransom, an Egyptian security official said last week.
Sand dunes of Egypt's Gilf el-Kabir near Libya, where the tourists were abducted [AFP]
They also want the ransom to be handed over to the German wife of the tour organiser.
The 11 European hostages comprise five Italians, five Germans and one Romanian.
The eight Egyptians include two guides, four drivers, a guard and the organiser.
The group was kidnapped on a desert plateau famous for prehistoric cave paintings.
Egypt's independent Al-Masry al-Yom newspaper quoted an anonymous German official as saying negotiations between German negotiators and the kidnappers had ended with the hostage-takers agreeing to release those captured in the near future.
An official at the German embassy in Cairo declined to comment.
Germany has kept quiet about its role in any negotiations, saying only that it has set up a crisis team.
The group was first moved across the border to Sudan to the remote mountain region of Jebel Uweinat, a plateau that straddles the borders of Egypt, Libya and Sudan.
On Thursday the kidnappers were reported to have moved into Libya, although officials there denied this.
There are conflicting reports about the nationality of the hostage-takers, with different sources saying they were from Sudan, Egypt, Libya, Chad or Djibouti.
One travel agent told the AFP news agency that in January a German group was attacked and robbed in the same area. They were abandoned in the desert with nothing but a satellite telephone. It is not known who carried out that attack.
Kidnappings of foreigners are extremely rare in Egypt.
In 2001, an armed Egyptian held four German tourists hostage for three days in Luxor, demanding that his estranged wife bring his two sons back from Germany. He freed the hostages unharmed.