Mend normally confines its operations to southern Nigeria
An unidentified armed group has launched an attack on the presidential palace in Malabo, the capital of Equatorial Guinea.
The West African country's ambassador to London accused Nigerian militants and said they had been repulsed.
But the Movement for the Emancipation of the Niger Delta (Mend) denied this, telling the BBC: "They are paranoid."
President Teodoro Obiang Nguema was not in his official residence in the capital at the time, say reports.
The country, sub-Saharan Africa's third biggest oil producer, has suffered decades of instability.
The shoot-out is said to have lasted for several hours from the early hours of Tuesday.
By daylight, armed security forces had deployed in Malabo and erected roadblocks to search vehicles and check passengers' identities, witnesses told AFP news agency.
Equatorial Guinean ambassador to London Augustin Nze Nfumu told the BBC's Focus on Africa programme: "I will categorically say there hasn't been any coup attempt in Equatorial Guinea at all."
He accused Mend and said the attackers had died when the security forces destroyed their boat.
Pouring scorn on Mend's denials, he added: "I don't think they [the attackers] are ghosts."
The ambassador said Mend had been behind two bank robberies in Equatorial Guinea's mainland city of Bata in December 2007.
But not everything is as clear as the government of Equatorial Guinea would like, says West Africa analyst Anthony Goldman.
In raids on Nigerian militant training camps, security forces have found people from Cameroon and Equatorial Guinea
Mend is a loose coalition of armed groups and it's not simple to say who is part of it and who is not.
"In raids on Nigerian militant training camps, security forces have found people from Cameroon and Equatorial Guinea," Mr Goldman told the BBC.
"There is concern about who was training people to do what."
Mend, which says it is fighting for a fairer distribution of wealth from Nigeria's oil, has normally confined its operations to southern Nigeria and its offshore oil installations.
But the militant group has been linked to more ambitious attacks in recent months on vessels off the coast of Cameroon.
"It seems more like a criminal act than something political. At the moment, the situation is calm," a Spanish foreign ministry spokeswoman told Reuters news agency.
Madrid's Radio Exterior de Espana Servicio Mundial reported another account which said forces loyal to British mercenary Simon Mann had tried to rescue him from a hospital he has been in for a few days.
Mann was sentenced to 34 years in jail last summer for his role in a 2004 coup plot in Equatorial Guinea.
President Nguema has ruled since 1979 after toppling his uncle in a coup.