The order on Sunday appeared to be an attempt to end the stand-off between Libya and the West over the prosecution of the five medics.
Libya's Supreme Court sent the case back to a lower court due to procedural lapses, Bulgarian state radio said on Sunday.
The six, in jail since 1999, were condemned to death by firing squad in May 2004 for what the Libyan government says was the deliberate infection of hundreds of Libyan children with the HIV virus in the port city of Benghazi.
Bulgarian state radio reported that they were sentenced to death for their role in "knowingly" infecting 426 Libyan children with the virus, which causes Aids.
The nurses and doctor say they are innocent and Sofia, Washington and Brussels have repeatedly asked for their release.
The medics were prosecuted for
infecting children with HIV
Bulgaria's president said he was hopeful for a breakthrough in the case after a deal was reached between Libyan and European negotiators.
The case had poisoned attempts by Muammar Qadhafi, the Libyan president, to rebuild ties with the West.
Europe and the United States accused Libya of making up the charges.