Puigdemont landed in Copenhagen from Belgium, where he had been living in exile with several ministers since declaring Catalan independence in October, sparking a constiutional crisis.
Spain's Supreme Court dropped an arrest warrant in December but the prosecutor has now applied for it to be reissued.
It remains unclear how Puigdemont could be sworn in again as regional president without returning to Spain and therefore putting himself open to likely arrest. Madrid also sacked his cabinet and imposed direct rule over the wealthy region.
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Puigdemont was to take part in a debate on Catalonia at the University of Copenhagen later Monday.
Carles Puigdemont has arrived in Denmark.
Danish authorities have not yet said whether they plan to turn Puigdemont over to Spanish officials.
Puigdemont has not yet commented on the Denmark trip, though on Friday he re-tweeted a Twitter post from Danish politician Pelle Dragsted saying he looked forward to welcoming Puigdemont to the Danish parliament the following week.
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There was no mention made today of a possible Pan-Korean bobsleigh team participating only in training runs before the Games. Under Kim Jong Un , North Korea has written the possession of nuclear weapons into its constitution.
In Spain, Pugidemont is facing charges of rebellion and sedition, but a judge withdrew the worldwide arrest warrant against him in December, partly because the former president was expected to return to Catalonia to have his day in court.
Speaker Roger Torrent is due to announce at around 1030 GMT the candidate to lead the regional government - and it is expected to be Puigdemont.
Rajoy has dismissed the possibility of long-distance rule by Puigdemont as absurd and Madrid has said it will contest any such decision in the courts.
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Amidst the government shutdown , now in its second day, Short appeared on Sunday's "Meet the Press" where he was questioned about its tone and content by host Chuck Todd.