Spokeswoman Victoria Nuland this week confirmed that Ntaganda turned himself in at the U.S. Embassy in Kigali.
The U.S. and Rwandan governments aren't party to the Rome Statute that created the International Criminal Court, which suspects Ntaganda of participating in crimes against humanity in the Democratic Republic of Congo.
"We do expect that the Rwandan government will cooperate in facilitating his transfer to the ICC" Nuland said. "It's a matter of working out the modalities, and that's going to take a little bit more time, it appears."
The International Federation for Human Rights, known by its French initials FIDH, said it's been nearly seven years since the ICC issued its first arrest warrants against the rebel leader. FIDH President Patrick Baudouin said proceeding at The Hague needed to start as soon as possible.
The Rwandan-born warlord, an ethnic Tutsi, served as the leader of the rebel March 23 movement, which is accused of war crimes during fighting in the Democratic Republic of Congo.
M23 allegedly has the support of the Rwanda government, an allegation Kigali denies.