Interior Cabinet Secretary Joseph Ole Lenku said the attackers destroyed Safaricom communication equipment before they undertook the new killings.
The CS said the attackers ensured the network was jammed so that locals could not raise alarm.
He said by paralysing communication, the attackers are sophisticated and seemed to know what they were doing.
“This is an elaborate war,” he said.
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.
Speaking at the venue, the Cabinet Secretary Secretary asserted that the killings were politically motivated, and they 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.
The CS, Principal Secretary Mutea Iringo and security chiefs including Inspector General of Police David 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.