Rajoy, addressing conservative Popular Party (PP) faithful in the southern town of Cordoba, said he hoped the separatists would choose someone “who sees things another way and who says, 'I am a political leader and that's why I am going to respect the law, because it's my obligation and that's what happens in democratic countries'.”
On Tuesday the Catalan parliament had been due to convene for the first time since regional elections in December that saw separatist parties retain their majority.
Puigdemont had been due for re-appointment as Catalan president, but the session was postponed at the last minute by parliamentary speaker Roger Torrent, also a separatist, exposing divisions in the independence camp.
Puigdemont remains in self-imposed exile in Belgium and faces arrest if he returns to Spain.
He headed to Belgium shortly after being sacked by Madrid over the Catalan parliament's independence declaration in October, which followed an unsanctioned regional referendum.
If he returns he faces arrest for leading the secession bid in the deeply divided northeastern region.
The Catalan separatists had considered renaming Puigdemont as regional president remotely, without the need for him returning to the country.
Catalonia's jailed former vice president Oriol Junqueras has suggested that Puigdemont could rule as a “symbolic” president with a fully functioning executive on site.
However, Spain's constitutional court has ruled out such a procedure.
On Sunday Junqueras's pro-independence ERC party sent a delegation to Brussels to study the possible way forward with Puigdemont.