Gedi has also offered amnesty to Islamic courts fighters.
Kenya sent troops and police to its northeastern border area, to which Islamic courts fighters have retreated after a two-week war in Somalia.
"Eleven Eritreans, Oromos and Somalis are already in the hands of Kenyan intelligence forces," Gedi said on Tuesday, a day after Somali troops backed by Ethiopian forces seized control of the last Islamic courts stronghold in the south of the country.
"The Islamists are still moving trying to cross the border into Kenya. So we expect more people to be caught later on ... Everybody is mobilised here and in Kenya to arrest them."
"It is very hard to establish if they are traders, refugees or fighters"
Kenyan police commander
Oromos, from southern Ethiopia, make up the backbone of the separatist Oromo Liberation Movement.
But Kenyan police said they were investigating eight men, including Eritreans and a Canadian, who were arrested as they tried to cross the Liboi border point, hours after the Islamic courts fighters fled their last stronghold in Kismayu, 500km south of the capital.
Among the eight there were three Eritreans, three Somalis, a Kenyan and a Canadian national of Ethiopian-Somali origin, they said.
Alarmed by the conflict moving south, Mwai Kibaki, Kenya's president, said late on Sunday that he will convene a summit as chairman of the Inter-Governmental Authority on Development (IGAD) regional group.
"All the ICU did was bring peace to a region engulfed in calamity for more then a decade"
A Somali, Somalia
Send us your views
A Kenyan police commander said of the arrested men: "All indications are that some of them were fighting, but we are still interrogating them, the Canadian is the only one saying he was a dealer of second hand clothes," .
"It is very hard to establish if they are traders, refugees or fighters."
The Kenyan government said it had boosted security along the 700km border with ground and aerial patrols to ensure that the Islamic courts fighters who fled the Somali town of Kismayu on Monday did not cross over. It had been asked by Somalia to close the border.
|Kenya hosts 160,000 Somali refugees [AP]|
Somali officials say they will pursue the Islamic courts fighters, who are believed to be in the Ras Kamboni area, a border forest near the Indian Ocean.
The northern stretch of Kenya's frontier with Somalia is already closely monitored for the transit of Somali refugees from the latest fighting in the south and centre of their country, in the wake of floods.
Kenya, which mediated the convoluted peace talks that ended in the creation of the Somali interim government two years ago, faces the prospect of receiving additional refugees.
The country already plays host to about 160,000 refugees from conflict in Somalia, which was carved up among rival clan leaders when Mohamed Siad Barre was overthrown in January 1991.