But it is unlikely to ease tensions between Madrid and Barcelona.
Catalan presidential hopeful Quim Torra says he will work toward building an independent republic if he is elected as the new chief of the restive region, as expected in a Monday parliamentary vote.
Separatist parties won regional elections in December.
One possibility that Torra suggested would be to have the so-called Assembly of Elected Officials symbolically vote-in Puigdemont as a president-in-exile.
Immediately after winning the vote, Torra said one of the goals of his new government would be to reinstate Puigdemont as "the legitimate president" of Catalonia.
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Quim Torra, a newcomer to politics who has campaigned fiercely for Catalonia's independence, was appointed regional president Monday vowing to keep fighting for a break from Spain.
"Everybody will win rights with the republic", Torra told lawmakers. But he appeared to outsource those legally problematic steps to ad hoc private institutions to be created by the separatists, a move that may spare his government further legal confrontation in the months ahead.
Torra's election by the regional parliament paves the way for a new government in Catalonia after months of political limbo.
"The Catalan republic is equality, liberty and fraternity". "Everyone can say whatever it finds opportune and convenient, but must comply with the law", Rajoy said.
Spanish daily El Pais summarised what Torra's leadership would look like elsewhere in Europe, saying it would be unfathomable that anyone with Torra's xenophobic and radical nationalist past - which included his penchant for exclusionary policies towards non-Catalans - could lead a police and paramilitary force of more than 17,000, collect taxes to run public services, educate children with respect for plurality, while also guaranteeing equality and free speech in the media using both the regional language, Catalan, and in Castillian, Spain's national language.
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The Spanish government called the speech confrontational and a member of the Catalan parliament for Rajoy's People's Party (PP), Andrea Levy, said on Monday in a television interview that Madrid would apply direct rule again if the new administration overstepped the law.
In a series of articles published in online media, for instance, he said it wasn't "natural" to speak Spanish in Catalonia. Spanish is more widely spoken than Catalan in the region, and Spanish speakers are overwhelmingly against secession.
A tweet he posted in 2012 said: "Spaniards only know how to plunder".
The Spanish legal system has charged Mr Puigdemont and other separatist leaders with a range of offences over their roles in the push push for independence. A separatist activist also couldn't be elected because he wasn't allowed to leave prison.
A Spanish Supreme Court judge has said Puigdemont's bid to secede should be regarded as "rebellion" because it used "violence", something rejected by separatists and questioned by German judges deciding on Puigdemont's extradition. Another nine have been jailed pending trial.
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He said: "I think this week, maybe there will be another conversation and we will see where we are for the next week". We just try to do the right things at the right time".
He was handpicked as a candidate by deposed leader Carles Puigdemont. CUP, the smallest of the three secessionist parties, agreed on Sunday to facilitate Torra's mandate with its four abstentions, but announced that it would join the ranks of the opposition, meaning it will be a struggle for the new Catalan Cabinet to get any legislation passed.