Ablyazov is wanted by Russia, Ukraine and Kazakhstan on embezzlement charges that he says were trumped up after he fell out with Kazakh President Nursultan Nazarbayev.
In Paris on Thursday Kasparov admitted he was not acquainted with the details of the case but had been asked by Ablyazov’s family and legal team to testify on the former bank governor’s likely treatment, based on the experience of opponents of Russian President Vladimir Putin.
"I think it will be a joke, a very bad joke, if the court accepts Russia's assurance about Ablyazov's safety," he said.
It is unheard of in France for a witness to be called in an extradition case but Ablyazov’s lawyers hope that Kasparov’s fame will lead to him being heard.
Citing Russia’s involvement in the Ukraine conflict, the chess champion, who has become a vocal critic of the Russian president, insisted that Putin would have no qualms about reneging on international obligations.
Ablyazov would certainly be handed over to Kazakhstan, with which France does not have an extradition treaty, Kasparov said, because Putin "needs Nazarbayev's support in Crimea, Ukraine and major geopolitical issues".
Kazakhstan, along with Belarus, is part of an economic union with Russia.
Ablyazov, who was head of the Kazakh BTA bank until he fell out with Nazarbayev and formed an opposition party, is accused of stealing billions of dollars in state and investors’ funds.
He was arrested at his Riviera mansion in July 2013.
The bank also had interests in Ukraine and Russia and a French court ordered his extradition to Russia because the embezzlement alleged by Moscow was much greater than that claimed by Kiev.
An appeals court blocked the extradition in April and the case must now be heard again by a court in Lyon.