"It is absurd to pretend to be the president of a region when you live abroad, and even more absurd to pretend that you are carrying out this function from abroad," Rajoy said in his end-of-year press conference in Madrid.
His remarks came a week after Catalan separatist parties claimed victory in a divisive snap election.
Madrid had called the poll after Catalan lawmakers declared independence on October 27, triggering Spain's worst political crisis since democracy was reinstated following the death of dictator Francisco Franco in 1975.
Following the declaration, Rajoy had sacked Catalonia's government, dissolved its parliament and stripped the region of its treasured autonomy.
Puigdemont fled to Brussels to avoid arrest over charges linked to rebellion, sedition and misuse of public funds.
Other independence leaders, including Puigdemont's former deputy Oriol Junqueras, are behind Spanish bars pending trial.
Rajoy reiterated Friday that a vote to choose a new Catalan president would take place within 10 days after the new regional parliament reconvenes on January 17.
Puigdemont's advisors are currently looking into whether he can run in next month's ballot from abroad.
Although the unionist Ciudadanos had the biggest share of the vote in the October ballot, three separatist groupings headed by Puigdemont retained their parliamentary majority.
The pro-independence parties have said they no longer plan to push for independence unilaterally and favour a negotiated settlement instead.
Rajoy, however, has repeatedly ruled out holding talks with Puigdemont.