What you need to know:
- The row between the two strongmen risks dragging in their neighbours, threatening economic integration and regional stability in an already conflict-prone swathe of the continent.
Kampala and Kigali traded accusations Saturday after Ugandan police accused Rwandan soldiers of entering the country and killing two men, further stoking tensions between the two countries.
Rwanda, however, disputed the Ugandan version of events and said the incident happened on its side of the border after officers were attacked with machetes.
"The government of Uganda protests in the strongest terms the violation of its territorial integrity by Rwandan soldiers and the criminal, brutal and violent act... against unarmed civilians," the Ugandan foreign ministry said.
Relations between Rwanda's President Paul Kagame and Uganda's Yoweri Museveni, once close allies, have turned deeply hostile in recent months with the pair making allegations of espionage, political assassinations and meddling against each other.
In a statement, Rwanda National Police said Rwandan security forces were attacked by people with machetes after stopping the suspected smuggler on a motorcycle after he crossed the border from Uganda.
"The officers shot two people, one Rwandan, who died instantly and one Ugandan who later died," it said. "The incident happened in Rwanda."
Ugandan police said earlier the raid occurred around 8:00 pm (1800 GMT) on Friday at a border post near the Ugandan village of Kiruhura in Rukiga district in the west of the country.
Police spokesman Fred Enanga said the soldiers entered "about 80 metres into Ugandan territory" in pursuit of a Rwandan on a motorbike.
"The victim resisted attempts to arrest him, and he was shot to the head and killed instantly," Enanga said, adding that a Ugandan who tried to intervene was also shot dead.
The soldiers then retreated back into Rwanda, he said.
"In this very instance, there was no justification for the illegal entry and use of deadly force by the Rwandan military, due to the presence of alternative, adequate and effective remedies available at our disposal," he said.
The border is porous and traders often smuggle goods from Uganda into Rwanda.
Rwanda drastically reduced imports from Uganda a few months ago and its citizens are banned from crossing over into Uganda.
Uganda however has not imposed tit-for-tat measures.
Enanga said Rwanda must "avoid acts of provocation". He said 44 Rwandans had been intercepted illegally entering southwestern Uganda recently and had been handed back in a "very peaceful manner."
The row between the two strongmen risks dragging in their neighbours, threatening economic integration and regional stability in an already conflict-prone swathe of the continent.
The standoff escalated dramatically in March when Rwanda publicly accused Ugandaof abducting its citizens and supporting rebels bent on overthrowing the government.
Museveni -- who has admitted meeting, but not endorsing, anti-Kagame rebels -- harbours his own suspicions about his erstwhile ally. His officials have accused Rwandans in Uganda of spying, and some have been detained or deported.