Lagos, Nigeria (CNN) Two International Red Cross Society (ICRC) aid workers kidnapped by a faction of Boko Haram in Nigeria's northeast may be executed Tuesday, the organization told CNN.

The ICRC issued desperate pleas to the Nigerian government to negotiate the release of the workers, adding that, "speed and urgency are critical."

Aleksandra Matijevic Mosimann, ICRC spokeswoman in Nigeria, told CNN they received an ultimatum from the militants on September 16 when the group also issued a threat against schoolgirl Leah Sharibu , whose parents confirmed to CNN she was "facing a death sentence."

Mosimann said the ICRC does not negotiate with terrorists but Boko Haram had reached out to them through "credible sources," about the deadline.

"We don't know the exact hour, but we have information from credible sources about this ultimatum after they killed one of our aid workers last month. That is why we have issued a public plea to the Nigerian government for their release," Mosimann said.

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