But the public prosecutor's office appealed against the move, arguing it violated an amnesty agreed by political parties in the spirit of national reconciliation in 1977, two years after Franco's death, for crimes committed under the general's rule.
It argued Garzon was "not competent to carry out this investigation", which should be up to "the courts of each region where such atrocities were committed".
On November 7 a panel of judges from the national audience, Spain's top criminal court, suspended the opening of the mass graves while it examined the public prosecutor's appeal.
In his ruling, Garzon conceded his court was not competent to take action for crimes against humanity against Franco or 43 of his associates because legal notification of their deaths had been issued.
He said he was thus transferring responsibility for the exhumations to the regional courts.
Garzon last month ordered the opening of 19 mass graves, including one near Granada where Spain's most widely acclaimed 20th century poet, Federico Garcia Lorca, is thought to be buried.
He ordered four more mass graves be opened this month.
Dozens of mass graves have been unearthed in recent years but the exhumations have been organised by relatives of the victims and volunteers, not by the state as was required by Garzon's ruling last month.
Historians have estimated that about 500,000 people from both sides were killed in Spain's 1936-39 civil war, which was sparked by Franco's insurgency against the democratically elected left-wing Republican government.
While the regime honoured its own dead, it left tens of thousands of its opponents buried in hundreds of unmarked graves across the country, according to victims' rights associations.