Kenya's army said it killed a regional commander from Somalia's al-Shabaab group, and possibly also a Briton who joined the militants, in fighting over the weekend.
Eleven Somali militants and two Kenyan soldiers were killed when al-Qaeda-linked al-Shabaab fighters attacked a military base in Kenya's northern coastal region of Lamu County, officials said.
Al-Shabaab confirmed the weekend attack, saying "many Kenyan soldiers were killed", without giving precise figures. It gave no details about any al-Shabaab members killed. The group often cites a higher death toll than officials.
Among those killed was al-Shabaab's Luqman Osman Issa, also known as Shirwa, blamed for leading attacks on Kenya's Mpeketoni area a year ago in which 65 people were killed, Kenya Defence Forces spokesman Colonel David Obonyo said on Monday.
"This is a big victory for us and also a major setback for al-Shabaab because now there is no mainstream commander in the Lamu area," he told Reuters, adding Shirwa's body was in a morgue in Mpeketoni.
He also said the dead may have included Thomas Evans, also known as Abdul Hakim, a Briton in his mid-20s who had converted to Islam aged 19 and later joined al-Shabaab. Obonyo said data about Evans and pictures publicly available "point at him".
"But we cannot be certain becomes sometimes looks can be deceiving. The necessary forensic investigations are being done including a DNA test I understand," he said, adding police were carrying out the tests.
Obonyo said another man of apparently of Caucasian or Arab origin was among the dead, while the others killed appeared to be from the region.
Al-Shabaab, which seeks to overthrow the Western-backed Somali government and impose its strict interpretation of Islamic law, has frequently targeted neighbouring Kenya in recent years, saying it is retaliating for Kenya's participation in an African Union peacekeeping force in Somalia.
In April, al-Shabaab militants raided a university in the northern Kenyan city of Garissa, killing nearly 150 students, and in September 2013 militants killed at least 67 people in an attack on Nairobi's Westgate shopping mall.