The two leaders used to be close allies
Rwandan officials say that three of their officers were at a routine security meeting just inside the Ugandan border when Lieutenant Charles Gahutu was kidnapped by Ugandan security personnel wearing trench coats.
"A commotion ensued during which his two colleagues managed to escape and flee back home, but Lt Gahutu was overpowered and bundled into the car," Police Chief Inspector Tony Kuramba told the Associated Press news agency.
Once close allies, Rwanda and Uganda have fought three times in the past two years for control of the mineral-rich area around Kisangani in the Democratic Republic of Congo.
Massing troops
Presidents Yoweri Museveni of Uganda and Paul Kagame of Rwanda met with British Prime Minister Tony Blair on Tuesday in order to diffuse tension.
Both countries accuse the other of massing troops near the border and sheltering dissident forces.
A spokesman for Mr Blair said that they had discussed international terrorism and economic development.
The two African leaders talked about tensions between their countries with British overseas development minister, Clare Short.
Major donor
Earlier this year, Mr Museveni wrote to Ms Short and reportedly requested British military aid in order to repulse a possible Rwandan invasion.
Britain is a major donor to both Uganda and Rwanda and is trying to calm the tensions which have existed since the fighting in Kisangani.
No comment was immediately available from Uganda on the alleged abduction but a senior advisor to Mr Museveni was optimistic about the London meeting.
"It should be possible to reach an understanding because all our points are reasonable. I would say the groundwork is very, very good," John Nagenda told the French news agency AFP before the meeting started.
Rwandans arrested
But the BBC's Helen Vesperini in the Rwandan capital Kigali said that the border incident did not bode well for the outcome of the London talks.
Two weeks ago, Uganda's anti terrorism task force arrested 10 Rwandan nationals in Kampala.
Among them were three deserters from the Rwandan Patriotic Army and a group of students from Makerere University.
The students were later released. Previous efforts to ease tensions between the once staunch allies ended in failure leading to speculation that they could go to war.
Appointment
In advance of the talks, Ugandan minister of state for defence Ruth Nankabira downplayed the significance of Mr Museveni's promotion of controversial military chief of staff Major General James Kazini to take overall charge of the army.
She said it was part of a reform programme.
Major General Kazini was in charge of military operations in DR Congo when Ugandan and Rwandan troops clashed in the north-eastern city of Kisangani in 1999.
The BBC Kampala correspondent, Anna Borzello, says that Rwanda has always blamed Major Kazini for the clashes.
She says that some Kampala diplomats see the appointment - and its timing - as provocative.
A United Nations report into the war in DR Congo named him as being one of those who had personally profited from the conflict by selling its natural resources.
Uganda and Rwanda were once the firmest of allies, with Uganda supporting Mr Kagame when his then rebel army fought its way to power in 1994.
They sent a joint force to the DR Congo in August 1998 but squabbles over business interests and personal rivalry led to the falling-out.