Serbia has said Ganic and a number of other people are suspected of war crimes, and blames them for the 1992 attack on a Yugoslav convoy in Sarajevo, when more than 40 soldiers were killed.
Ganic, a former Bosnian deputy president, is accused of ordering the killing of more than 40 Yugoslav army soldiers retreating from Sarajevo at the start of the war.
"This is a case that has not inspired Interpol to pursue a valid arrest warrant, it has not inspired the Hague tribunal to look into it"
Daughter of Ejup Ganic
Emina Ganic, his daughter, told Al Jazeera her family disputes the charges.
"This is a politically motivated issue and it is a clear abuse of law and of English courts and of a justice system that exists in this country.
"This is a case that has not inspired Interpol to pursue a valid arrest warrant, it has not inspired the Hague tribunal to look into it.
"So we have one last attempt where the Serbians are ... trying to present this case for the third time at an opportune moment, and I assure you they will not be successful."
His arrest at Heathrow airport was condemned by a top Bosnian official, who said the action would strain ties between the two nations.
"Just when we tried to improve ties with Belgrade ... then Belgrade makes such a move that worsens relations to a great extent," Zeljko Komsic, the Croat chairman of Bosnia's tripartite presidency, was quoted as saying by SRNA agency.
Haris Silajdzic, Bosniak presidency member also said Ganic's arrest would undermine Bosnia's sovereignty.
"This is not the first attempt to relativise and set equal blame," he said.
"There will be more, but we will fight to defend the rights of our citizens and the dignity of our resistance to the aggression that was launched on Bosnia."
Ganic, a Muslim member of Bosnia's presidency during the 1992-95 war, appeared at the City of Westminster Magistrates Court after his arrest.
He was remanded in custody following the hearing and will appear in court again on March 29, police said.
Al Jazeera's Aljosa Milenkovic, reporting from Belgrade, said Ganic had been detained at the London airport once before on February 26, while on his way to Libya.
He was, however freed a day later, prompting the Serbian Interpol office to demand an explanation from the UK.
Serbia must now provide full papers to support its extradition request before a date can be fixed for a hearing, a spokesman for Britain's foreign office said.
A judge will then consider whether there are any bars to the extradition.
Bosnia's inter-ethnic war between its Croats, Muslims and Serbs claimed some 100,000 lives. During the conflict Belgrade politically and militarily backed ethnic Serbs.