Mr Kagame was leader of the mainly-Tutsi rebel force, which came to power in Rwanda following the genocide, when up to a million Tutsis and moderate Hutus were murdered by Hutu extremists.
Chief prosecutor Carla del Ponti said it is the first time members of the victorious side in the civil war will be charged for crimes allegedly committed during 1994, the year of the Rwandan genocide.
Speaking in Arusha, Tanzania, where the international court on Rwanda sits, Ms del Ponti said she had discussed this with the Rwandan President, Paul Kagame, who had offered full co-operation.
Mr Kagame was leader of the mainly-Tutsi rebel force, which came to power in Rwanda following the genocide, when up to a million Tutsis and moderate Hutus were murdered by Hutu extremists.
So far, only suspects supporting the ousted mainly Hutu regime have been tried in Arusha.
After the war, the Tutsi-led Rwandan Patriotic Front (RPF) came to power in Kigali.
Sheltering suspects
Ms del Ponti says two African countries have been sheltering the most wanted suspects.
While the prosecutor did not name the countries, official tribunal sources said Kenya and the Democratic Republic of Congo were the chief suspects.
"I depend on the goodwill of the governments in the search, arrest and transfer of these subjects, " Ms del Ponte said.
She said some of the suspects have been allowed to travel freely to certain countries and have been issued passports with new identities and nationalities.
Ms del Ponte said the tribunal may soon issue indictments against RPF soldiers who allegedly took revenge in the aftermath of the 1994 genocide, or while attempting to stop it.
The BBC's correspondent, Liz Blunt, says there has been a long history of suspicion between the Rwandan Government and the international war crimes tribunal, which has, so far, only convicted seven people.
On one occasion, it let a major suspect slip through its fingers because it had not followed correct legal procedures.
The Rwandans were so incensed that for a time they would not let Ms del Ponte into the country.