The Eritrean government says the men were detained as they tried to leave Eritrean waters without permission and searches then found a weapons cache.
The private security firm the men work for says they were en route to provide security for ships in the region.
A media release attributed to Eritrea's foreign ministry alleges the four Britons have "fully admitted" illegally entering sovereign Eritrean land bearing arms.
'Attempted to flee'
It says the men have also admitted trying to escape from the Eritrean port of Massawa and have "expressed regret for their actions".
The statement says the Eritrean navy fired warning shots at the men's boats after they made "an attempt to flee" without legal clearance on 24 December.
Eritrean officials searched the island of Romia "where a cache of sniper weapons fitted with silencers, telescopes, distance-monitoring equipments were secured," the statement said.
We deeply regret the situation we find ourselves in
Protection Vessels International Employer of detained men
"Moreover, night-vision binoculars equipped with GPS, together with poison-tipped bullets, bullet-proof vests, specialized communication equipments, as well as V-SAT satellite telephones were seized during the search."
Protection Vessels International (PVI), the private security firm the men work for, says the men had stopped off to resupply and that the incident was a misunderstanding.
In a statement, PVI said the men had realised the "potentially threatening presence of an armed security company making a normal port call for resupply", so had decided to off-load some of its equipment on the island first.
"This equipment included weapons, optics, radios, helmets, body armour and navigation equipment, standard issue for anti-piracy operations, PVI's primary function," PVI's statement said.
The firm added: "The company acknowledges that its personnel mishandled the situation and we deeply regret the situation we find ourselves in.
"We simply needed to conduct a port call and we very much regret any misconception of presenting a threat to the president of Eritrea and to the Eritrean people."
BBC News - FCO presses Eritrea for access to Britons held as spies
The private security firm the men work for says they were en route to provide security for ships in the region.
A media release attributed to Eritrea's foreign ministry alleges the four Britons have "fully admitted" illegally entering sovereign Eritrean land bearing arms.
'Attempted to flee'
It says the men have also admitted trying to escape from the Eritrean port of Massawa and have "expressed regret for their actions".
The statement says the Eritrean navy fired warning shots at the men's boats after they made "an attempt to flee" without legal clearance on 24 December.
Eritrean officials searched the island of Romia "where a cache of sniper weapons fitted with silencers, telescopes, distance-monitoring equipments were secured," the statement said.
We deeply regret the situation we find ourselves in
Protection Vessels International Employer of detained men
"Moreover, night-vision binoculars equipped with GPS, together with poison-tipped bullets, bullet-proof vests, specialized communication equipments, as well as V-SAT satellite telephones were seized during the search."
Protection Vessels International (PVI), the private security firm the men work for, says the men had stopped off to resupply and that the incident was a misunderstanding.
In a statement, PVI said the men had realised the "potentially threatening presence of an armed security company making a normal port call for resupply", so had decided to off-load some of its equipment on the island first.
"This equipment included weapons, optics, radios, helmets, body armour and navigation equipment, standard issue for anti-piracy operations, PVI's primary function," PVI's statement said.
The firm added: "The company acknowledges that its personnel mishandled the situation and we deeply regret the situation we find ourselves in.
"We simply needed to conduct a port call and we very much regret any misconception of presenting a threat to the president of Eritrea and to the Eritrean people."
BBC News - FCO presses Eritrea for access to Britons held as spies
