The Renewed Front for the Liberation of the Cabinda Enclave (Flec) said on Tuesday its military wing had "downed a helicopter in the area of Miconge, about 90 kilometres from the town of Cabinda" on May 13.
The Angolan government had the previous week announced a police helicopter had "disappeared" following "bad weather" in the area.
The statement, signed by Estanislau Miguel Boma, the Flec's chief of staff and its military wing, spoke of a "resumption in fighting between the Angolan armed forces and the forces of resistance in Cabinda".
"Twenty soldiers from the Angolan army died and several others were injured following violent fighting which started on May 18" in the regions of Buco Zau and Necuto north of Cabinda town, it said.
It said eight rebel soldiers died in separate fighting in April in the Mikuma and Mviedi regions, adding that the separatist forces then attacked the areas, "killing three civilians and fuelling an exodus of the local population".
On Saturday, Angolan police spokesperson Carmo Neto said a "police helicopter carrying two crew members and a police border guard disappeared on May 13 in Cabinda's frontier region of Necuto after crashing into a mountain due to bad weather".
Despite intensive searches by the army, police and locals, the helicopter has not been found.
In late 2002, some 30 000 Angolan troops were deployed in Cabinda, an enclave between Angola, Congo and the Democratic Republic of Congo and home to 120 000 people, which has been the scene of unrest and separatist conflict since the 1960s.
Angola emerged from 27 years of civil war in April 2002 and has since become one of Africa's top oil producers, with United States firms active in the enclave.