A British jihadist fighting for Somalia's Al-Qaeda affiliate, the Al Shabaab, is believed to have been killed in a thwarted attack on a Kenyan army base on Sunday, a Kenyan defence spokesman said.

The Briton is believed to be among a group of militants who launched a pre-dawn raid Sunday on a Kenyan army base in Baure, close to the border with Somalia.

Two Kenyan soldiers were killed and at least 11 Al Shabaab fighters died in the shootout, among them two "Caucasians", according to Kenyan defence officials.

"All the available data, including photographs, points to it being Thomas Evans. There is an investigation going on with forensics and DNA to confirm his identity," Kenya Defence Forces spokesman Colonel David Obonyo on Monday.

If confirmed, Evans' death will be the first reported case of a British Islamist militant being killed on Kenyan soil.

Evans, in his mid-20s and also known as Abdul Hakim, is a Muslim convert whose family lives in Buckinghamshire in southern England. In 2011, he reportedly travelled to Somalia to join Al Shabaab.

The British embassy in Nairobi said it was "seeking to confirm reports" that a Briton had been killed.

"We are aware of the reports," a British embassy spokesman said.

Kenya's Interior ministry posted a notice on its official Twitter account showing side-by-side photographs of Evans and a dead militant who resembled him, under the banner, "Thomas Evans aka Abdul Hakim Killed. Kenya Stands Strong!"

In a separate attack, also on Sunday, dozens of Al Shabaab gunmen briefly took over a village in Lamu county. Kenyan officials said a major security operation was underway on Monday to pursue both groups of attackers.

The raids came on the anniversary of attacks that began in mid-June 2014 in which close to 100 people were killed in a series of armed assaults on the town of Mpeketoni and surrounding villages.

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The attacks in Mpeketoni, close to the once-popular holiday island of Lamu, led to a collapse in tourism on Kenya's coast after foreign governments warned their nationals against travel to the area.

On Monday human rights groups said that Kenya's security response to the Mpeketoni massacres had been marked by beatings, arbitrary detentions and theft.

Under pressure in Somalia where it has for years been fighting to overthrow the internationally-backed government, Al Shabaab is now increasingly targeting Kenya.

In the group's deadliest attack to date, four gunmen killed at least 148 people, mostly students, at a university in Garissa in early April. In September 2013, four Al Shabaab gunmen killed at least 67 people in an assault on the Westgate mall in the capital Nairobi.

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The Al Shabaab were once a magnet for foreign volunteers, but their capacity to recruit has in recent years been eclipsed by the rise of Islamic State militants in Syria and Iraq, while several foreign Al Shabaab members have fallen victim to in-fighting and purges.

The highest-profile British Al Shabaab supporter is terror suspect Samantha Lewthwaite, known as the "White Widow". She is wanted in Kenya on charges of being in possession of explosives and conspiracy to commit a felony dating back to December 2011. Her alleged accomplice, Jermaine Grant, is on trial in Mombasa accused of planning attacks on tourist hotels.

Lewthwaite, a 31-year-old Muslim convert, is the widow of Germaine Lindsay, one of four Islamist suicide bombers who attacked the London transport network on July 7, 2005, killing 52 people.

Despite repeated rumours there has been no confirmed sighting of her since she gave Kenyan police the slip in Mombasa in 2011.