Puigdemont and his suporters say he can rule from self-imposed exile in Belgium, where he fled to in October to avoid arrest for his part in organising a banned referendum on a split from Spain and the consequent declaration of independence.
Prosecutors were calling for Puigdemont to be arrested in Denmark, where he traveled on Monday.
Spain's state prosecutor is seeking his arrest in Denmark.
A previous European arrest warrant issued by Spain was withdrawn in December, before a Belgian court decided whether or not to extradite Puigdemont and four of his former Cabinet members.
Puigdemont's Junts per Catalunya (Together for Catalonia) party emerged as the largest separatist force in a December 21 regional election that returned a majority of seats in parliament to pro-independence parties.
Freezing Rain Coming to Toronto, Ottawa
Drivers in those areas were being warned of likely icy roads Monday evening, as well as the possible for power outages. Several millimetres of rain could accumulate.
Spanish Foreign Minister Alfonso Dastis said the matter was for judges to decide. He attacked court decisions to jail separatist leaders on remand and said the sacking of his government by Spanish Prime Minister Mariano Rajoy was an attack on democracy.
He is not obliged to agree to the request to reissue the warrant.
"President Puigdemont never dismissed the possibility of presenting and submitting his candidacy in person", the lawyer told Catalonian public television, adding that his client was "aware of the risks he faces".
As Spain's legal system wrestled over arresting Puigdemont, the ousted leader's name was put forward as a candidate for president.
The leader of Catalonia's parliament has nominated Carles Puigdemont to a new term as president, adding another twist in the story of the separatist leader who was ousted from power by Spain previous year. He is also due to meet the Danish parliament's foreign policy and European Union affairs committee during his visit to Copenhagen this week, according to foreign policy spokesman of the opposition Red-Green Alliance, Nikolaj Villumsen.
It is not clear whether the Spanish Supreme Court judge Pablo Llarena, who is handling the case, will grant it.