Eritrea has denied claims its forces were behind the kidnap of five British people in Ethiopia on Thursday.
The embassy staff and their relatives were sightseeing near the disputed border region between the countries when they went missing.
The president of Ethiopia's Afar region said Eritrean troops had taken them to a military camp in Eritrea.
The Foreign Office did not confirm the report, and the Ethiopian ambassador to the UK refused to "finger point".
Several Ethiopian drivers and translators who had been accompanying the Britons are also missing.
Ismael Ali Sero, head of the Afar region in the north of Ethiopia, said cars used by the sightseers were set on fire in the early-morning raid on their camp.
He said about 25 Eritreans in military uniform marched the group 12-18 miles (20-30 km) to the town of Waime in Eritrea.
Money, mobile and satellite phones were also stolen, he added.
A senior Ethiopian official in the ruling party, who asked not to be named, said a herder saw the British group at the Ara-ta military camp in Eritrea and reported it to the Ethiopians.
But Berharnu Kebede, Ethiopian ambassador to the UK, told Sky News: "We are not in the business of finger pointing at any group or individual or any country.
"For us the priority is to secure the safe return of these people, so no official from the Ethiopian government has said that."
Yemane Gebremeskel, the director of Eritrean President Issaias Afeworki's office, said Mr Ismael's claim was "crazy".
"No one is involved in any business of kidnapping," he told AFP.
"Of course there are no Eritrean soldiers in Ethiopia."
A peace deal was struck in 2000 but the two countries have yet to define the status of the border, patrolled by UN observers.
French nationals 'safe'
About 10 British officials, thought to include an expert hostage negotiator, have been meeting at the British embassy in the capital, Addis Ababa, in an attempt to find the missing Britons.
The government emergency planning committee Cobra met on Friday to discuss the issue.
Ethiopian police said the tourists were kidnapped, along with 13 Ethiopian drivers and interpreters, about 800km (500 miles) north-east of Addis Ababa.
The area is one of hottest places on Earth (picture: Sam Vader)
The Italian foreign ministry told the AFP news agency that one of those kidnapped had dual British-Italian nationality.
Seven French nationals who had been thought to be among the kidnapped group are safe and well, the group's travel company, Origins Ethiopia, has said.
More intrepid visitors to the Afar region like to tour the Danakil Depression, one of the lowest and hottest places on Earth known for its salt mines and active volcanoes.
But bandits and rebel groups operate there and tourists are advised to travel there with an armed guard.
The Britons' tour operator Tony Hickey said local reports suggested three of his vehicles were hit by anti-tank grenade launchers in Hamed Ela near the border.
He told the BBC many foreign tourists had visited the area in the last year and the Eritrean authorities could have acted to "embarrass" the Ethiopian government.