Al-Shabab militants have overrun an African Union military base outside the southern Somali town of el-Ade.
The Islamist group says it has taken “complete control” of the AU camp and killed more than 60 Kenyan soldiers.
Residents told the BBC that al-Shabab had raised its flag at a camp for Kenyan troops and said insurgents had paraded bodies through the town.
But Kenya’s army spokesman said it was a nearby Somali base that was stormed and Kenyan troops counter-attacked.
The number of casualties on both sides was not known, Kenyan military spokesman Col David Obonyo said in a statement.
He told the BBC that reports of high Kenyan casualties were “normal propaganda from al-Shabab”.
Kenya contributes more than 4,000 troops to the 22,000-strong AU force that is in Somalia helping the UN-backed government battle al-Shabab, which is part of al-Qaeda.