Judge Pablo Llarena said in a decision published Thursday that he's revoking the worldwide arrest warrants against the six, in what the Catalan separatist movement was likely to regard as a major victory against Spain's central authorities.
Judge Pablo Llarena revoked the European and global arrest warrants previously issued against Professor Ponsati and the other five Catalan politicians.
Puigdemont is one of 13 separatist leaders accused of the most serious charge rebellion over their role in Catalonia's failed secession bid last October.
Spain's top judge Pablo Llarena says that in doing so, the German court showed a "lack of commitment" to the case and violated the arrest warrant rules.
In Spain, rebellion carries a maximum sentence of 30 years in prison, while misuse of public funds has a maximum sentence of 12 years.
The Spanish court also dropped European arrest warrants for five other Catalan pro-independence leaders living overseas.
The decision meant that if he were to be extradited, Spain would only be able to try him on charges approved in the extradition order, and not rebellion.
"We will fight to the end and win", Puigdemont said on Twitter.
The other fugitive politicians apart from Puigdemont are Antoni Comin, Meritxell Serret and Lluis Puig, who also fled to Belgium, Clara Ponsati, who is in Scotland, and Marta Rovira, who is believed to be in Switzerland.
The Spanish judiciary's decision to withdraw the arrest warrants demonstrated the "weakness" of its charges, Puigdemont said.
The Spanish court rejected that proposal, lifting the arrest warrant altogether.
"It's excellent news, with regards to my client Clara Ponsati, and obviously for Puigdemont. but we tread cautiously", lawyer Aamer Anwar told the Reuters news agency.
They were preparing to argue that the European Arrest Warrant was invalid, that the Spanish government could not comply with the relevant legal requirements, that the prosecution was essentially political in nature and that to return Prof Ponsati to Spain would be incompatible with her human rights.
Mr Sanchez has taken a softer approach toward Catalonia than his predecessor Mariano Rajoy, meeting Catalan president Quim Torra for talks earlier this month.