Another attack in Mpeketoni last night left at least 15 people, including two police officers killed, police have confirmed.
A Nation journalist at the scene counted nine bodies, who residents said were picked out from their houses by name by the attackers.
They were then then lined up at a swampy Kaisare area and shot in the head at point-blank range.
Interior Cabinet Secretary Joseph Ole Lenku initially said the attackers destroyed Safaricom communication equipment before they undertook the new killings.
He said by paralysing communication, the attackers are sophisticated and seemed to know what they were doing.
"This is an elaborate war," he said.
However, Mr Lenku later clarified that the Safaricom outage in Mpeketoni as caused by power failure and inaccessibility of alternative fuel following the attack.
He said initial outage lasting three hours on Monday was caused by power failure. A subsequent outage lasting for more than six hours from midnight Monday to Tuesday morning was caused by delay in getting fuel to the Safaricom station.
The CS said fuel had to be sourced from Garsen in Tana River County because of the damage to the petrol station in Mpeketoni, which was burnt during the Sunday attack.
A curfew placed by security officers led to further delay.
Three houses were torched in Mapenya village in the same area, and police Tuesday were trying to establish if this was in retaliation for the attacks.
Angry residents gathered at Lake Kenyatta area Tuesday morning called for immediate action as they sought audience with Mr Ole Lenku.
They had earlier barricaded the main road to Lamu as they demanded for extra security in the area.
Speaking at the venue, the Cabinet Secretary Secretary asserted that the killings were politically motivated and was related to land dispute between communities there.
He said the government had reliable intelligence that similar attacks might occur in other parts of the country.
The al Qaeda-linked Shabaab militant group have already claimed responsibility for the Monday night attack.
"We carried out another attack last night. We killed 20 people, mainly police and Kenyan wildlife wardens. The commandos have been going to several places looking for military personnel," Shabaab's military spokesman, Abdulaziz Abu Musab, told AFP by telephone.
Mr Lenku said new officers have been brought to Lamu County, and hinted that government officials in the county might be sacked in relation to the killings.
Lamu County Commander Leonard Omollo, District Commissioner, area OCS and other security officials are to be interdicted, he said.
The CS, Principal Secretary Mutea Iringo and security chiefs including Inspector General Kimaiyo and the two deputy Inspector Generals Grace Kaindi and Samuel Arachi are in the area in the wake of the killings that started on Sunday night.
Forty eight people were massacred in the initial attack by dozens of gunmen who arrived in the sleepy town in several minivans on Sunday.