At least 13 people have been killed in new attacks in Kenya's coastal county of Lamu, the same area where some 60 people were massacred last month, the Kenyan Red Cross said Sunday.

The organisation said nine people had died and one person was missing in the locality of Gamba, while four people had been killed in Hindi, a trading post near Lamu island. The areas were attacked late Saturday, authorities said.

There were no further details from officials on the attacks, with Kenya's National Disaster Operations Centre only saying in a brief statement on Twitter late Saturday that gunfire had broken out.

A spokesman for Somalia's Shebab rebels issued a statement late Saturday claiming that the Al-Qaeda-linked group's fighters had carried out another attack in the area.

"The attackers came back home safely to their base," Shebab military spokesman Abdulaziz Abu Musab said, saying that 10 people had been killed in the attack.

The Shebab also claimed responsibility for last month's attack at Mpeketoni, saying it was in retaliation for Kenya's military presence in Somalia as part of the African Union force backing the country's fragile and internationally-backed government.

Survivors of the massacre in Mpeketoni and a similar attack the following night in a nearby village reported how gunmen speaking Somali and carrying Shebab flags killed non-Muslims and said their actions were revenge for Kenya's presence in Somalia.

Kenyan President Uhuru Kenyatta, however, denied that the Shebab were involved and instead blamed "local political networks" and said that the victims had been singled out because of their ethnicity.

The had attackers appeared to target Mpeketoni because the town is a mainly Christian settlement in the Muslim-majority coastal region, having been settled decades ago by the Kikuyu people from central Kenya, the same tribe as Kenyatta.

Police also arrested alleged separatists from the Mombasa Republican Council, a group that campaigns for independence of the coastal region, as well as the governor of Lamu county, who is an opposition politician.

The unrest in the coastal region has badly dented Kenya's tourist industry -- a key foreign currency earner and massive employer for the country -- at one of its traditionally busiest times of the year.