Bemba faces five counts of war crimes and three counts of crimes against humanity, with specific charges including murder, rape and torture.
The judge set November 4, as an initial date for the start of a hearing for the confirmation of charges.
Aime Kilolo Musamba, Bemba's lawyer, objected to alleged violations in the execution of his client's arrest warrant, and Bemba complained about his holding conditions.
"The conditions aren't the best, not what I had hoped for ..." Bemba told the court.
Bemba was transferred to the detention unit of the court on Thursday from Brussels, where he was arrested on an ICC warrant on May 24.
He is the court's fourth detainee along with fellow Congolese Thomas Lubanga, Mathieu Ngudjolo Chui and Germain Katanga.
In Bemba's arrest warrant, fighters from his Movement for the Liberation of Congo (MLC) are alleged to have attacked the civilian population, committing rape and torture on "a systematic or widespread scale".
As commander-in-chief, the prosecution seeks to hold Bemba criminally responsible.
Musamba, Bemba's lawyer, said on Thursday, that his client welcomed the chance to prove his innocence.
"This provides us with the opportunity to go to The Hague and present the elements of defence that we have which will help establish that Mr Bemba has no legal responsibility in this affair," he told AFP news agency.
Luis Moreno-Ocampo, ICC prosecutor, welcomed Bemba's extradition to The Hague.
"Justice is coming for the victims, for the victims of the Central African Republic, for the victims of massive sexual violence worldwide," he said.
Hope for justice
"This is a significant moment for Bemba's victims in Central Africa," said Geraldine Mattioli, from the Human Rights Watch, who was present at Friday's proceedings.
"One hopes that the prosecution will expand the accusations to include crimes committed by the MLC in the Democratic Republic of the Congo," she said.
It could be months or even years before a trial date is set as a host of procedural matters will have to be settled first.
Lubanga, the subject of the first case before the ICC, was transferred to the court in March 2006, but his trial has yet to start.
Bemba, 45, heads a business empire and had been living in exile in Portugal, where he fled under United Nations protection following a shoot-out with the presidential guard in DR Congo in March 2007, which killed more than 200 people.
That followed defeat to his rival Joseph Kabila, the current DR Congo president, in elections the previous year.
The ICC was set up six years ago as a permanent world court mandated to try war crimes, crimes against humanity and genocide.