The ICRC, which does not pay ransoms, earlier said it had not been directly involved in discussions on the extremists' demands.
Reacting via a statement, Mohammed said the government is deeply pained by the incident.
"Saifura and Hauwa were killed because they are considered as Murtads (apostates) by the group because they were once Muslims that have abandoned their Islam, the moment they chose to work with the Red Cross, and for us, there is no difference between Red Cross and UNICEF", the group added.
"My colleagues and I in the Nigerian Senate remain committed to continuing working with our Armed Forces to find a lasting solution to these senseless killings by insurgents and improve our security infrastructure", said Senate President Bukola Saraki on his Twitter page. The UN chief stressed the importance of protecting those who provide humanitarian assistance to millions in northeast Nigeria.
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Before her murder, one of the health workers, aifura Hussaini Ahmed Khorsa, was executed by the sect in September.
The ICRC workers had been in the north east of Nigeria in the town of Rann where a military outpost had given some protection to the 80,000 refugees refugees displaced by the 9-year-old conflict and violence of the Islamist insurgency.
The terrorists, according to the report have said they'll keep Alice and Leah Sharibu, the Dapchi schoolgirl who wasn't released by the terrorist sect because she refused to renounce her faith, as slave. More than 100 girls have since been released or found. It is thought she continues to be held because she is Christian. Her mother in recent weeks has said her life was in danger.
The Spokesperson for President Muhammadu Buhari, Garba Shehu, gave a terse SMS reply, saying: "Lai Mohammed is doing a statement".
On Sunday, the International Committee of the Red Cross (ICRC) called on the Nigerian authorities to ensure the release of the abducted medical staff, as the deadline set by militants to kill them was approaching.
President Buhari also spoke with Peter Maurer, the President of the ICRC, extending condolences on the loss of the midwife.