The death toll is rising, floods have turned estates into rivers, disrupted transport and destroyed crops.
They warned the move would have a harmful impact on human rights and refugee protection.
Other European countries, including Austria and Germany, are also looking at agreements to process asylum seekers abroad.
It is believed that Somalia and Turkey signing a marine and defence cooperation agreement paved the way for the oil deal.
Dr Mathuki presided over the EAC Secretariat at a time the bloc marking an expansion trajectory, overseeing the entry of DRC and Somalia.