Together with Greenland, the Faeroes have long sought further autonomy while allowing Denmark to handle their foreign affairs and defense.
Roger Torrent, the newly elected speaker of the Catalan parliament, on Monday formally proposed Puigdemont as the candidate to form a government. Speaking to a crowded auditorium at the University of Copenhagen, he said that he sought to regain his old job as Catalonia's president because supporters of secession had won the most seats in the recent election.
A Faeroese lawmaker invited Puigdemont to the Danish Parliament on Tuesday.
Puigdemont, who is in Denmark to give a speech, potentially faces decades of jail in Spain for leading Catalonia's independence drive.
Spanish prosecutors on Monday morning asked for the activation of a European arrest warrant for exiled former Catalan leader Carles Puigdemont, who has travelled from Belgium to Denmark to attend a conference at a university.
The Catalan parliament's legal experts have said that any presidential contender has to be physically present, but Puigdemont insists he has the legitimate mandate of the people to rule.
Madrid sacked Puigdemont and his entire government, and it dissolved the parliament following the declaration. The judge might not re-issue the arrest order for the same reasons. "Outside, for the moment, his movements are free within the European Union, but we'll see", Dastis said earlier on Monday in Brussels.
The refusal comes after the speaker of the Catalan parliament nominated Mr Puigdemont to lead the regional government.
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Charged with rebellion, sedition and misuse of public funds, Puigdemont now faces arrest if he returns to Spain over his role in the independence drive.
The Danish state prosecutor declined to comment.
Pablo Llarena, the judge in charge of the case against Puigdemont, will rule on the request to reactive the warrant.
Torrent said Puigdemont is the only candidate with enough backing to attempt a government following regional elections last month.
"Mr. Puigdemont is subject to a process in Spain".
The court said in a statement it would postpone the decision until the Catalan parliament has been fully restored to normal activity, Reuters reported.
However, Spain's Supreme Court rejected prosecutors' request to re-issue a European warrant, on charges of sedition and rebellion, for his arrest on Monday.
Several fellow separatist lawmakers are already in custody in Spain over their role in the regional parliament unilaterally declaring independence on October 27 and Spain's general prosecutor office said Saturday that "it's inadmissible that the privilege of parliamentary immunity should be interpreted as impunity".