"It is correct that a parliament can debate calmly the candidate for the presidency".
Puigdemont was released after he was arrested in Germany, pending a decision on extradition to Spain.
Rajoy says on Saturday that his government upholds and abides by court rulings in Spain and elsewhere.
The other charge against him, misuse of public funds will be reviewed by Germany after Spain presents their case.
Rajoy's position was not shared by the leading politician of his conservative Popular Party in Catalonia. "We always said we were ready", Puigdemont said.
Carles Puigdemont, the former president of the government of Catalonia, has urged Spain to allow Catalonia to form their regional government headed by Jordi Sanchez, who is now in prison for rebellion charges in a press conference Saturday.
"My plan is to remain in Berlin, it's my residence now until the end of this process", Mr Puidgemont said on Saturday at a hastily organised news conference in the German capital. A German court refused to extradite him on charges on rebellion, but is considering Spain's request to extradite him on the lesser charge of misuse of funds.
Trump Rips Dem Joe Manchin: 'You're Not Getting Help'
The crowd applauded - as did Representative Evan Jenkins, a Republican challenging Manchin - at the dig at the incumbent senator. In a tweet, the president credits "the strong immigration laws of Mexico and their willingness to use them".
Separatist politicians are considering a second attempt to elect Sanchez after being emboldened by a German court's decision not to extradite Puigdemont.
"This opens a new opportunity of dialogue".
Puigdemont, granted bail after German judges ruled he could not be extradited on charges of "rebellion" brought by Spain, thanked prison staff as he emerged to cheers and people waving Catalan flags.
Misuse of public funds carries a sentence of up to eight years in Spain, while a rebellion sentence can reach 30 years. He had been there since March 25, when he was arrested crossing the border from Denmark. He was trying to drive from Finland to Belgium, where he had been living since fleeing to escape arrest in Spain.
The deposed leader left a prison in the northern state of Schleswig-Holstein on Friday afternoon after posting €75,000 (£65,000) in bail.
Germany's Minister of Justice, Katarina Barley, said "it will not be easy" for Spain to prove that charge and if it fails, "then Puigdemont will be a free man in a free country, that is, Germany".
He says the Spanish government "met its obligations" by imposing direct rule on Catalonia after Puigdemont and other separatists organized the independence referendum a year ago. The court, however, has not ruled out extradition on the charge of "embezzlement".