Unknown gunmen sneaked into the remote Kiwayu Safari Village resort in Kenya by night, killed publishing executive David Tebbutt, 58, and kidnapped his wife Judith, 56, both from the UK, before escaping undetected by speedboat on Sunday.
Kenyan police said the gang are likely to have fled to Somalia.
"Preliminary investigations and communications we had been between us and experts from Interpol and other relevant agencies indicate that the gunmen seem to be acting on orders from a larger group of militia men," said an anti-terrorism source, who declined to be named.
"They are definitely part of a larger group that seems to have been preying on tourists, mostly high spenders and VIPs. They are taking advantage of the fact that Mkokoni area doesn't have a single speedboat and relies mostly on Kenya Wildlife Service personnel."
"We have arrested one man and he is assisting the police with their investigations into the murder of the British man and the kidnap of his wife. The suspect was arrested on Monday within Lamu district," deputy police spokesman Charles Owino told Reuters on Tuesday.
On Tuesday morning Kenyan security and police patrolled the coastline at the Kiwayu Marine Reserve as what appeared to be a government helicopter landed on the island. Journalists were not allowed access to the island.
No group has yet claimed responsibility but the way the attack was carried out and the proximity of the Somali border points to the involvement of Somali bandits or pirates.
"So far we have yet to get any communication from the kidnappers but they are most likely in Somalia," CID director Ndegwa Muhoro said.
However the anti-terrorism officer said it would be difficult to pin down the culprits if they are indeed in Somalia, an anarchic country where Al-Waeda-linked Al-Shabaab militants controls large swathes of the southern-central regions.
"It is a bit difficult trying to locate a gang that is in a country that has no government. They could take hours, days, weeks, or even months before they communicate," he told Reuters.