Sudanese President Omar Al-Bashir, wanted by the ICC on genocide charges, was permitted to attend Museveni's inauguration.
The ICC has launched a preliminary examination of the violence that has killed over 400 people.
At least 300 people died in clashes between the Nigerian Army and the country's main Shiite movement.
Cultural heritage destruction, like the Sufi mausoleums of Timbuktu, robs peoples of their identity.
Human rights lawyers allege that the Nigerian president has committed crimes against humanity against pro-Biafran activists.
The former president is accused of crimes against humanity during violence after the 2010 election.
Prosecutor Fatou Bensouda intends to investigate possible crimes committed during the five-day Russia-Georgia War in 2008.
The complaints relate to Israel's conduct during the 2014 Gaza war and settlement construction.
The Palestinian authority is seeking an inquiry into last summer's Gaza conflict, a move deeply opposed by Israel.
The UN Human Rights Council launched an inquiry in September after ISIS seized large swathes of northern Iraq.
Wife of ex-president Laurent Gbagbo tried for role in 2011 post-election crisis in which 3,000 were killed.
Graham said existing U.S. legislation "would cut off aid to the Palestinians if they filed a complaint" against Israel.
The move could lead to cases being brought against Israeli or Palestinian leaders
"It is an escalatory step that will not achieve any of the outcomes most Palestinians have long hoped to see for their people."
The move means the court could take jurisdiction over crimes committed in the Palestinian territories.
President Kenyatta is the first sitting leader to appear at the International Criminal Court, facing charges of crimes against humanity
Palestinian Foreign Minister Riad al-Malki said there was "clear evidence" of war crimes by Israel during its offensive in Gaza