Museveni said his allowing Kenyan Turkana's to settle in the said area has remained a destabilising factor for his country.
The order comes after a Ugandan martial court in April sentenced thirty-two Kenyans to 20 years each in prison for illegally possessing firearms and ammunition.
The Turkana herders from Orum in Lodwar were convicted after pleading guilty and sentenced to serve jail terms in Moroto Government Prison in Northern Uganda.
Asked for a comment, Kenya's Foreign Affairs Cabinet Secretary Alfred Mutua said he would not comment on the matter as the government has not been officially served with the order.
But Museveni said he had ordered the said Turkana to never smuggle guns in Uganda but just graze their cattle.
However, the Ugandan Head of State said they ignored the directive and rather continue to raid disarmed Karimonjong, rape and kill them.
They are said to have raided 2,245 cattle from the Jie, killing three geologists, one officer, and a soldier that was guarding them.
"I now direct that this Turkana nonsense must stop. They must never come to Uganda with guns and anybody who does so, must be arrested and charged with terrorism by a Court Martial," he said.
Museveni said the killers of the Geologists must be handed to Ugandan authorities for a murder trial.
He said all the guns that have been smuggled guns must be handed over and through the co-ordination of the Governments of Kenya and Uganda, the killers must perform a blood settlement known as kukaraba to the families of the deceased.
Museveni said the price of the kukaraba cannot be the traditional one, of a few cows.
"It must be adjusted to the full value of what the deceased would have contributed in his/her life, which life was cut short by those criminals," he said.
Museveni further said through the coordination of Kenya and Uganda governments, theTurkana must bring back to the victim communities the number of cattle equal to those stolen from them.
Here, he said caution should be exercised because his people could be exaggerating the numbers.
Stay informed. Subscribe to our newsletter
"In order to ease the task of cattle identification, the Kenya Government and Uganda should co-ordinate on cattle-branding to show district and sub-county of the respective cattle populations," he said.