Judith Tebutt was kidnapped on Saturday night during an incident in which her husband David was shot dead on Kiwayu Island.
Coast Provincial police commander Aggrey Adoli who is leading the security operation told Capital News that more security forces had been mobilised for the search at the Kenya-Somalia border.
He said the hunt is being conducted jointly by the police and military using all resources at their disposal, including helicopters and boats.
“We have not made any success yet but we hope to find her safe. We are using all the resources available,” Mr Adoli said on telephone from the Kenya-Somali border near Kiunga.
Police suspect she may have been abducted by Al Shabaab extremists and the search is being concentrated at the Kenya-Somalia border.
“We are appealing to members of the public to volunteer any information that can help us find her safe,” Mr Adoli said.
Police have not publicly admitted they are pursuing the involvement of the al-Shabaab extremists but knowledgeable police sources speaking on condition of anonymity said the couple was likely attacked by the militants.
“We suspect they were al-Shabaab and that is why the search is being concentrated at the Somalia border,” one senior police officer said, referring to the group waging an insurgency against the Western-backed government in Somalia.
On Sunday, Police Commissioner Mathew Iteere said the couple was attacked at about midnight on Saturday at the Kiwayu Safari Village, a popular tourist lodge in the Kiunga marine reserve.
The couple had been in the Maasai Mara for a week before they flew to Lamu and checked into the resort late on Saturday.
“Apparently, we are told they were the only ones in the lodge at the time of the attack which took place hours after they checked in,” the police commissioner told journalists on Sunday at a press conference at the police headquarters.
A caution posted on the Foreign Office website advised Britons against going within 50 kilometres of the Kenya-Somalia border.