London (CNN) -- Kenyan police have launched an investigation into the killing Sunday of a British man and the abduction of his wife from a remote safari lodge on the coast, near the border with Somalia.
"We sent a signal to all the police stations so that we can be more vigilant, especially regarding our vital installations," Kenyan Police Commissioner Mathew Iteere told reporters Sunday in Nairobi.
"Already we have sent more reinforcements, especially in North Eastern province, more roadblocks, especially leading to or coming from North Eastern province and Coast province. Those we have done, and we are going to continue, not just because of this incident. We had done it because of the anniversary of September 11."
About 12:30 a.m. Sunday, bandits attacked the couple, who were staying at Kiwayu Safari Village, a tourist resort on Kiwayu Island in Kiyunga division of Lamu west district on the coast, he said.
During the attack, David Tebbut was shot dead and his wife, Judith Tebbut, was abducted, Iteere said. The couple had arrived at the hotel Saturday afternoon after spending a week in the Masai Mara game reserve in southwestern Kenya. They were the sole guests in the hotel, which has cloth doors, he said.
"From what we can be able to gather, he resisted, and that's why he was shot dead," Iteere said. "Maybe they wanted to take the two, but he resisted and that's why he was shot dead."
Iteere said the motive was not known. "We are treating it just as a bandit attack," he said.
A travel website lists rates at the 18-cottage resort as beginning at $400 per night.
A maritime security source aware of the situation said Sunday that Islamic militants probably took Judith Tebbut by boat toward Ras Kamboni in Somalia.
"We are working to secure the safe and swift release of the British national who has been kidnapped and ask those involved to show compassion and release the individual immediately," the British Foreign Office said in a statement.
"We continue to advise against all but essential travel to within 30 kilometers of Kenya's border with Somalia," the office said in an advisory that cited previous attacks by Somali militia in Kenya. Much of the south of Somalia is controlled by al Qaeda-linked Al Shabaab rebels.
In a statement, Minister of Tourism Najib Balala said the ministry "is working together with the relevant security organizations to ensure that the perpetrators of this crime are brought to justice. A team of security personnel are already on the ground and a massive manhunt of the perpetrators of this heinous act has been launched."
More than 1 million tourists, 174,000 of them Britons, visited Kenya last year, he said.
Kenya Tourist Board Managing Director Muriithi Ndegwa said in a statement, "At this point in time we wish to reassure all our local and overseas travel trade that the safety of our tourists is paramount and that the government has proper machinery in place to ensure high level security of our tourists."
CNN's David Wilkinson contributed to this report.