Human Rights Watch has urged Jordan to prevent Sudan's president from entering the country or to arrest him when he arrives for the 28th Arab League Summit.
The International Criminal Court issued two arrest warrants for Omar Al-Bashir in 2009 and 2010 over his role in Sudan's counterinsurgency operations in the impoverished Darfur region.
The Sudanese leader also faces charges of crimes against humanity including genocide and war crimes.
According to Elise Keppler, associate international justice director at Human Rights Watch:
Jordan would be defying its international obligations as an ICC member if it allows Al-Bashir to visit without arresting him.
"Welcoming an ICC fugitive would undermine the Jordanian government's recent efforts to strengthen the country's rule of law."
Jordanian authorities have not confirmed whether Al-Bashir will be allowed to make his first visit to the country as a figure wanted by the ICC.
Some members of the international court have stated that Al-Bashir will face the likelihood of arrest if he enters their countries whereas others have called for Sudan to send representatives on their behalf instead or relocated meetings to accommodate the president.
Since October 2014, around two million people have been affected by the conflict, with more than 500,000 displaced and 250,000 forced to flee to South Sudan and Ethiopia.
Fighting intensified in January 2015, when Al-Bashir's government tried to regain control of opposition-held territory ahead of the April 2015 general elections.