The dead included a personal bodyguard for a local governor whose convoy was targeted.
The deaths came a day after Kenya's police chief Joseph Boinnet announced that al-Shabab extremists based in Somalia were stepping up attacks inside the country.
He said al-Shabab is under pressure from African Union troops supporting Somalia's government, which recently declared a new offensive against the extremist group.
In the first incident, a police vehicle heading toward the border town of Liboi was blown apart by an improvised explosive device, North Eastern Regional Coordinator Mohamud Saleh said.
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Two other officers were injured in the attacks. Al-Shabab, which has ties to al-Qaida, claimed responsibility for the first attack in a report by its news agency, saying it had killed at least five Kenyan police officers, according to the SITE Intelligence Group, which monitors extremists.
In the last two weeks, attacks by al-Shabab in Kenya's Garissa and Mandera counties have increased after a lull. Last week, an improvised bomb killed four people in a vehicle, including a child.
Kenya's troops are part of the AU force there. Kenya has managed to stop the frequency of al-Shabab attacks in its capital, Nairobi, and major towns, but human rights groups say the government uses methods such as extrajudicial killings that can fuel revenge attacks.
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