In a video released in recent hours viewed by local reporters, the militants said Liman deserved to be killed because she had abandoned Islam by working for the ICRC.
Leman, a nurse with the International Committee of the Red Cross (ICRC), was kidnapped by the armed group in March along with two other medical workers in Rann, Borno State in the country's northeast.
Ms Khorsa was killed last month and the faction holding her - known as the Islamic State's West Africa Province - threatened to kill another hostage by Monday if their demands were not met.
"We urge the Nigerian authorities to continue to tighten the noose around the terrorists until the last of those being held captive by Boko Haram is released as the desperate action on the part of the terrorists must not be allowed to slow down the operations meant to restore normalcy to the region".
An urgent plea to the largest ISIS-linked extremist group in Africa had come from the ICRC to spare Liman's life, Nigeria's government said late Monday.
He said the government was shocked and saddened by the killing of the aid worker, despite the actions it took and the widespread appeal to save the young woman.
In a statement issued by its embassy in Abuja, U.S assured Nigeria of its continuous support in the fight against terrorism. "It is now seven months and 16 days only to be told that yesterday she was executed by the insurgents".
Earlier this summer, the United Nations released a report alleging that the Nigerian government paid a ransom for the release of the schoolgirls, but not for Sharibu because she is not a Muslim.
A schoolgirl who is also being held was among 110 girls kidnapped from a school in the town of Dapchi in February.
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.
"We will continue to pray for her safety with a hope that one day she will return home and restored all our happiness".
Since March 1, the ICRC has repeatedly made representations to the government of Nigeria about the abducted healthcare workers, at different levels.