TVGE, the official news channel in the tiny west African nation, said security forces had killed “a mercenary… and used gunfire to disperse them (others) in the forests along the border”.
The report did not mention how many “mercenaries” were involved or for how long clashes lasted.
Hours earlier, Security Minister Nicolas Obama Nchama told public radio that the country had thwarted a “coup” in December that was aimed at toppling Obiang, Africa’s longest serving president.
“Mercenaries… were recruited by Equatorial Guinean militants from certain radical opposition parties with the support of certain powers,” he said.
The plot had been prevented thanks to an operation carried out “in collaboration with the Cameroon security services”, Obama said.
The announcement came after Cameroon on December 27 arrested 38 heavily-armed men on the border with the tiny state.
Two days later, Equatorial Guinea’s ambassador to France, Miguel Oyono Ndong Mifumu, referred to the incident as an “invasion and destabilisation attempt”.
The suspects, taken into custody in a bus on the border, had rocket launchers, rifles and a stockpile of ammunition, according to his office.
On Saturday, the 75-year-old Obiang said “a war” was being prepared against his regime, “because they say I have spent a lot of time in power”.
Obiang has been president for more than 38 years.
He took power in a coup on August 3, 1979, ousting his own uncle, Francisco Macias Nguema, who was shot by firing squad. He was re-elected to a fifth seven-year term in 2016.
Equatorial Guinea is one of sub-Sahara’s biggest oil producers but a large proportion of its 1.2 million population still lives in poverty.
His regime regularly comes under fire from rights groups for violent suppression of the opposition, civil society groups and the media.