It's a rare critique of a former laureate, amid a war that has killed thousands and displaced millions since breaking out over a year ago.
In the past week airstrikes killed at least 73 civilians in Tigray, according to aid workers.
In a statement on Thursday (January 13), Norwegian Nobel committee chair Berit Reiss-Andersen said the "humanitarian situation is dire".
And that Abiy - who was given the award in 2019 - bears a "special responsibility" to "end the conflict and contribute to making peace."
Abiy's spokesperson Billene Seyoum said the prime minister had taken up this "special responsibility" and was engaged in "putting an end to not only the past year's conflict" but also the "destabilizing activities" of the Tigray People's Liberation Front.
But underscoring the domestic challenges Abiy is facing, pressure was also applied from a different quarter on Thursday.
Eskinder Nega was among several opposition leaders released from prison last week.
At a press conference he said Abiy needs to fulfil his oath - that is by taking back control of Tigray and uniting the country.
"We will nag him", he said. "We will not leave him alone until he ensures the sovereignty of the country is respected."
