The rule change may impact the trial of Kenyan president Uhuru Kenyatta which is due to begin in February.
According to the amendment, a defendant who is summoned to appear may request the court in writing for permission to attend all or part of the trial by videoconference.
The court will rule on a "case-by-case basis," but the amendment also gives the court more room to excuse an accused from part of a hearing if that person is "mandated to fulfill extraordinary public duties."
The rule change was introduced at the request of the African Union which has been at loggerheads with the ICC over its indictments of Kenyan president Uhuru Kenyatta and his deputy William Ruto.
African delegates argued that elected leaders needed to be near their people, especially in a country like Kenya which is facing an islamist terrorism threat.
However, human rights organizations strongly criticized the rule change. "Such political decisions endanger the independence of the Court and may put the Judiciary in a difficult position, where it might not be able to apply a rule that is inconsistent with the Rome Statute," said Paulina Vega, vice-president of the International Federation for Human Rights (FIDH).
"FIDH and its member organisations will remain highly mobilised against possible States attempts to undermine the Rome Statute and the ICC judges integrity," said FIDH President Karim Lahidji.
Meanwhile Amnesty International said the amendment was a threat to the principle that everyone is equal before the law.
For numerous observers, the amendments adopted by the ASP introduce exceptions to the rules in response to a political situation stemming from the election of Kenyatta and Ruto in March 2013.
On Tuesday, just before the changes to the Statute were adopted, the Chamber handling the Kenyatta case had ruled that the Kenyan president could only be absent from his trial under exceptional circumstances and that this authorization did not constitute a rule.