They said the tribunal only needed to prove that there are "reasonable grounds to believe" al-Bashir was responsible for genocide.
Luis Moreno-Ocampo, the chief prosecutor at the ICC, also called for the case to be sent back to the ICC's pre-trial chamber.
He told Al Jazeera: "We believe it's a mistake.
"They requested a level of evidence beyond any doubt and this is the level of evidence [needed] for the conviction, not for the beginning of the trial.
"This is the main reason we are appealing.
"I think we will win. I believe we have a strong case to win this appeal. I believe we have a case of genocide."
Mark Ellis, the chairman of the International Bar Association, told Al Jazeera that charging an individual with genocide was a "complex legal process".
"It requires the prosecutors to prove the individual had a specific intent to destroy an ethnic group," he said.
"Whether or not the prosecutor is successful really will have no bearing on the case itself. It will move forward."
Al-Bashir has denied the prosecution's allegations and has refused to recognise the court's jurisdiction.
Leaders of the African Union said on Friday they would no longer co-operate with the ICC and would not arrest and extradite the Sudanese president.
Al-Bashir was indicted over his alleged role in the conflict in Darfur, which the UN says has displaced an estimated 2.7 million people.
The UN says up to 300,000 people have died since the conflict began in 2003 between ethnic minority rebels and the Sudanese government.
Sudan's government disputes the figures, saying 10,000 people have been killed.