An al-Shabab military spokesman says the armed group has killed about 25 Kenyan police officers in a village north of the town of Garissa, where fighters killed 148 students in April.
However, Kenya's interior ministry via its official Twitter account said no police officers were confirmed dead.
Sheikh Abdiasis Abu Musab said on Tuesday that 20 officers were killed when al-Shabab fighters ambushed them on Monday night in Yumbis village, 70km north of Garissa, while more officers were killed when a police vehicle hit a landmine planted by the fighters, Reuters reported.
"We took all their weapons. There were some Kenyan forces that escaped in the course of the ambush fighting," he said, adding that five police vehcles had been burnt.
Al Jazeera's Mohammed Adow said Garissa police had confirmed that 20 officers had been killed in the attacks.
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Police patrolling between Garissa and the Dadaab refugee camp hit an improvised explosive device, or IED; and a second group of officers reacting to a distress call from the first attack then came under fire.
Some of the survivors fled the scene and arrived in a nearby refugee camp, our correspondent added.
An official earlier told Al Jazeera on condition of anonymity that at least five police officers were missing and four vehicles had been torched.
Al-Shabab has carried out several attacks in Kenya in retaliation over Kenya's military involvement in Somalia.
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Somalia has been unstable since the collapse of Siad Barre's government in 1991, and the country's new government is being supported by the 22,000-strong African Union force.
The armed group carried out its deadliest attack in Kenya earlier this year, when its fighters massacred 148 people in a day-long siege of a university in Garissa.
The attack on the university was the deadliest on Kenyan soil since the 1998 bombing of the US embassy in Nairobi, which killed more than 200 people.
After the Garissa attack, al-Shabab warned of a "long, gruesome war" unless Kenya withdraws its troops from Somalia, as well as warning the government in Mogadishu it would continue to attack them on home soil.
Source: Al Jazeera and agencies