But Nigeria's Information Minister Lai Mohammed earlier announced the latest death as a deadline expired and said the government was "shocked and saddened" at the killing, calling it "dastardly, inhuman and ungodly".
Hauwa was one of the three health workers abducted by Boko Haram in March 2018 during a raid on a military facility in Rann, Kala Balge, an area heavily affected by violence. She was abducted along with Liman and Alice Loksha, a nurse who worked at a center supported by the United Nations children's agency.
The government identified her as Hauwa Mohammed Liman, who had been working in a hospital supported by the ICRC. "Based on our doctrines, it is now lawful for us to do whatever we want to do with them".
According to a statement by Garba Shehu, the president's spokesman, in a telephone call, Mr Buhari commiserated with Hauwa's family and assured her father that the Nigerian government did everything possible to save his daughter's life, expressing sadness that all the efforts turned out unsuccessful. The splinter terrorist group has killed hundreds of soldiers in attacks in northeastern Nigeria in the last couple of months.
An ICRC spokeswoman told Reuters on Monday: "We are hearing devastating reports that Hauwa has been executed".
"The terrorists threatened to kill Leah in October if they don't get any response to their demands".
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Nigerian President Muhammadu Buhari, who declared that defeating extremism was a top priority when he took power in 2015, last week sent three Cabinet ministers to meet with the families of Sharibu and the abducted health workers, his office said.
"The gruesome killing of the aid worker has confirmed that Boko Haram is a group driven by mindless wickedness and one that must be collectively dealt with by the entire world. However, we will keep the negotiations open and continue to work to free the innocent women who remain in the custody of their abductors".
We are not sure of the exact time or hour when it expires, but are extremely anxious for lives of the Hauwa and Alice.
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.
He also thanked all the friendly governments and the clerics across religious lines, that have continued to work with Nigeria for the safe release of the abducted women. They were praised for volunteering to work in a unsafe area while many others fled or chose to remain in safer communities.