"The terrorists threatened to kill Leah in October if they don't get any response to their demands".
Islamist extremists in Nigeria have killed a medical aid worker held hostage since March. "However, we will keep the negotiations open and continue to work to free the innocent women who remain in the custody of their abductors".
ICRC also said it made sustained and committed efforts to secure the release of the three health-care workers, including a last-minute plea for mercy on Sunday to the Islamic State's West African province group, to no avail.
"The news of Hauwa's death has broken our hearts", ICRC's regional director for Africa, Patricia Danzi, said.
"It is painful to note that despite efforts by the Federal Government who opened a negotiation channel immediately and put all possible efforts on table to secure an agreeable bargain for the safe release of the abductees, unfortunately, Mr Speaker, the Boko Haram sect took a terrible path of executing these helpless and selfless voluntary health workers who gave their time on earth for the care and wellness of devastated Boko Haram victims", he added.
An ICRC spokeswoman told Reuters on Monday: "We are hearing devastating reports that Hauwa has been executed".
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The ICRC said it did not have official confirmation, adding: "We desperately hope not".
The Nigerian government called the murder "inhuman and ungodly".
Boko Haram uses kidnapping as a weapon of war, abducting thousands of women and girls and forcing young men and boys to fight in their ranks.
More than 20,000 people have been killed and two million others forced to flee their homes in northeastern Nigeria since Boko Haram launched a campaign in 2009, aimed at forming a breakaway Islamic state.
Ms Liman was abducted in March in Rann, Borno State.
In an emailed statement on Monday, the Nigerian government confirmed the killing, and reacted to criticism that it had not done enough to save the victims by saying: "the Federal Government did all within its powers to save her life". More than 100 girls have since been released or found.
Analysts believe this breakaway faction has a new hardline leadership after another internal struggle and is responsible for the recent killings.