However they have been unable to elect a candidate for the presidency.
Torra's election and the formation of a new government would close the latest chapter in the Catalan crisis, which reached its height previous year when regional leaders held a disputed referendum on breaking away from Spain and then declared independence.
Led by Mr Puigdemont's party, the pro-independence groupings won a narrow majority in the regional parliament.
However, Mr Torra could still be elected in a second round of voting to be held on Monday in which only a simple majority in the 135-seat regional parliament is needed, provided the far-left CUP party can be persuaded not to vote against his candidacy.
In a widely shared video on social media, Puigdemont suggested Quim Torra for president, signalling a potential end to months-long wrangling over a new regional government.
From December 2017, the Catalan Parliament already four times tried to form a government, but all candidates for the post of Prime Minister are either in prison or outside of Spain and can not return to the country for prosecution.
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In the year to March, annual consumer price inflation was 2.5 percent, well below the bank's projection of nearly 3 percent. They repeated their calls for a rise to 0.75 per cent to avoid more "abrupt" policy action further down the line.
Backing unilateral independence over the negotiated exit favoured by larger separatist parties, the CUP has previously broken ranks with the pro-independence block.
Since Catalonia's last election in December, four attempts to form a government have failed because the presidential candidates were either in self-imposed exile or in custody. "He makes a call to clash, to have more confrontation", she said. "Our group proposes member of parliament Quim Torra to be president of the Catalan government so he can take on this responsibility in the next few days and so that a government can be formed immediately", Puigdemont said.
Puigdemont, who first fled to Belgium, was detained in Germany in March after Spain issued a European arrest warrant against him.
Madrid wants to extradite him to Spain to try him on charges of rebellion - which carries up to 30 years in prison - and misuse of public funds for his role in the secession drive.
Puigdemont is now in Berlin, awaiting a decision from a German court on whether he will be extradited to Spain.