Ethiopian officials have accused Eritrean forces of kidnapping five British citizens and 13 Ethiopians who were touring a remote region near the African countries' long-disputed border, then taking the group to a military camp in Eritrea.
The claims could not be independently verified.
The group went missing on Thursday while travelling in Ethiopia's Afar region, a barren expanse of ancient salt mines and volcanoes 800 km north-east of the capital, Addis Ababa.
The BBC, quoting unidentified government sources, said there was a "national security dimension" to the disappearance of the Britons, all of whom are employees of the British embassy in Addis Ababa or their relatives.
Britain's foreign and defence ministries would not comment on the BBC report.
Ismal Ali Sero, head of the Afar administrative region, said about 25 Eritrean "commandoes" kidnapped the British citizens along with their Ethiopian drivers and translators on Thursday night. He cited local investigators.
But a senior Ethiopian official in the ruling party, who asked not to be named, also said Eritreans were behind the kidnapping.
He said a herder saw the British group at the Ara-ta military camp in Eritrea and reported it to the Ethiopians.
Herders in Afar frequently travel between the two countries, which have had consistently strained relations since Eritrea gained independence from the Addis Ababa government in 1993 following a 30-year guerrilla war.
Tour operators in the area also said they were being told by police Eritreans in military uniforms kidnapped the Britons and burned down the house where they were staying, along with several vehicles.
A spokeswoman for the British embassy in Addis Ababa, speaking on customary condition of anonymity, said she had no information on the kidnappers: "We do not know where they are or who is holding them. We are not prepared to speculate."
Earlier on Saturday, a team of British officials arrived in Ethiopia to help in the hunt for the missing group.
Britain's Foreign Office in London would provide no further information on its efforts, but the Press Association said the officials, known as a rapid deployment team, were thought to include a hostage negotiator and medical staff.
It was also reported a special forces rescue team was on standby to free the captured party by force if necessary.
British Foreign Secretary Margaret Beckett on Friday confirmed five "members of staff, or relatives of members of staff, at our embassy in Addis Ababa" were missing in the desert region which borders southern Eritrea.
British Prime Minister Tony Blair was being kept aware of developments and Beckett said the government was doing all it could to resolve the situation.
The Italian foreign ministry said one of those kidnapped had dual British-Italian nationality.
The group was abducted early on Thursday morning at a camp in Hamed Ela, some 50 km from the Eritrean border in Afar region, their tour operator and Ethiopian police said.
Three vehicles in which they were travelling have been found destroyed near where they were abducted, Tony Hickey, their tour operator, told AFP.
Also on Saturday, the head of an Afar tour agency said the driver for seven missing French tourists have called his company to say everyone was "safe and well" and had not been kidnapped.
Sources, including French diplomats and local businessmen, had been reporting the French were kidnapped.
"They were not kidnapped, but they heard there had been some trouble so they avoided the area. That is why we thought they had been kidnapped, because we had lost contact altogether," said Samson Teshome, head of the Origins Ethiopia tour group. He said it was unclear where the tourists had been since Thursday and why they had been out of contact.
Dominique Gautier, spokesman for the French embassy in Addis Ababa, said he couldn't confirm the account.
"We know many people are saying they are safe but I have no direct contact with them so I cannot confirm this," he said.
Bandits and a small rebel group operate in Afar, where the famous Ethiopian fossil of Lucy, the earliest known hominid, was discovered in 1974.
The Ethiopian government requires tourists to travel in Afar with armed guards; the British and French groups were believed to have complied.