Ordonez, 36, is wanted by the Spanish authorities to stand trial over his alleged involvement in moving materials, weaponry and men from France to Spain, for the purposes of terror activity, and gathering information on public figures including politicians.
In 2008, a French court sentenced Ordonez, in his absence, to five years in prison on other charges.
Ordonez, who denies all the allegations, arrived in Scotland in 2001 and had been working as a delivery driver.
At Edinburgh Sheriff Court yesterday, Sheriff Alistair Noble agreed to a request from Ordonez’s defence to continue the hearing until September 7, with a preliminary hearing set for August 23. Ordonez was again remanded in custody.