Rwanda's spy chief refused to consent to his transfer to Spain at a London court hearing on Thursday after President Paul Kagame slammed his arrest on a Spanish-issued warrant as "absolute arrogance".
The 54-year-old general Karenzi Karake, known as "KK", was wearing a yellow and green jumpsuit.
He raised his clasped hands as he entered the dock to cheers from supporters in the courtroom.
Karake's defence team included Cherie Blair, the wife of former British prime minister Tony Blair, who works as a special consultant to Kagame and is involved in charity initiatives in Rwanda.
Asked whether he consented to his extradition, Karake replied: "I do not".
District judge Quentin Purdy said that a full extradition hearing would take place on October 29 and 30.
The hearing was still to decide whether he would remain in custody until then.
The general, part of a circle of top military officers in the former Rwandan Patriotic Front (RPF) rebel movement, was arrested at London Heathrow Airport by British extradition officers on Saturday.
A Spanish judicial source said he stands accused of "crimes of terrorism" linked to the killing of nine Spanish citizens in Rwanda in the 1990s.
British police, however, said the 54-year-old was arrested for alleged "war crimes against civilians".
A judge at Spain's National Court on Wednesday "made a formal request" for Britain to hand over the suspect, a judicial source said.
A small demonstration took place outside Westminster Magistrates Court in London ahead of the hearing.
"We want them to free KK. His detention is unfair, he actually stopped the genocide," said Mutesi, a 24-year-old Rwandan woman taking part.
"I don't think that he is guilty at all. This is a political case," she said, as demonstrators carried placards reading: "Stop Humiliating Africa" and "UK, USA, Stand Against Spanish Indictments".
- 'Absolute arrogance and contempt' -
The RPF ended the 1994 genocide by Hutu extremists which left an estimated 800,000 people dead, mostly Tutsis. Atrocities were also committed against Hutus.
The Rwandan government has condemned the detention of Karake, who has been head of the intelligence service since 2011, branding it an "outrage".
Hundreds of protesters marched on the British embassy in the Rwandan capital Kigali on Wednesday demanding Karake's release.
"Absolute arrogance and contempt is the only basis for this arrest," Kagame said in a speech to parliament on Thursday.
"We cannot accept that people treat us this way just because they can."
Describing Karake as a "freedom fighter" Kagame accused European countries of racism and seeking to humiliate Rwanda -- and other Africans -- in order to veil their own complicity in the 1994 genocide.
"They want to mask their responsibility by saying it's not us, it is savages of Africa who killed each other," he said.
Kagame questioned the right of Britain to act on the Spanish indictment, which accuses Karake of mass ethnic killings of Hutus in the wake of the 1994 genocide.
"What right does this country have to arrest him in this manner? None of them have any basis other than absolute arrogance," he said.
European Arrest Warrants are valid throughout the European Union, requiring member states to arrest and extradite suspects to the issuing country.