The application follows an announcement by the court's chief prosecutor last year that he would investigate allegations of mass rape, torture, looting and ritual cannibalism in northeastern DRC.
A court statement said prosecutor Luis Moreno Ocampo had received a letter signed by Kabila referring to him the situation in the DRC, "in which it would appear crimes covered by the competence of the court have been committed."
The court was competent because the alleged offences had been committed since the new tribunal came into being in July 2002.
"By this letter, the DRC refers the situation to the prosecutor and requests him to conduct investigations to establish whether one or more persons should be charged with these crimes," the statement said.
It said the DRC had agreed to cooperate with the ICC.
The Hague-based ICC is the first permanent international tribunal trying cases of genocide, war crimes and crimes against humanity.
In July last year, the court prosecutor announced his intention to investigate the situation in Ituri in northeastern DRC, because of what he described as the urgency and gravity of the situation there.
He said he would investigate alleged atrocities including among other things gang rape, torture, looting and cannibalism.
Kabila's letter represents a further stage in the procedure.
Under the Statute of Rome creating the ICC, the prosecutor must now establish whether there are reasonable grounds for beginning an investigation in DRC, the statement said.
Ituri has been torn since 1999 by clashes between rival ethnic groups claiming tens of thousands of lives - Sapa-AFP.
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