Spain's Prime Minister Mariano Rajoy has given him until Monday to clarify his position - and then until Thursday to change his mind if he insists on a split - threatening to suspend Catalonia's autonomy if he chooses independence.
But far-left Catalan political group CUP called on Puigdemont to make an unequivocal declaration of independence in defiance of the deadlines.
"If (the central Madrid government) wants to continue to threaten and gag us, they should do it to the Republic that has already been claimed," the party said.
The CUP only holds 10 seats in the 135-seat Catalan parliament. But Puigdemont's minority government relies on its support to push through legislation and cannot win a majority vote in the regional parliament without its backing.
The wealthy region's intention to break away after a referendum has plunged Spain into its worst political crisis since an attempted military coup in 1981 and could hurt economic growth targets for next year, the deputy prime minister said.
"If there were no quick solution to this issue we should be forced to lower expectations of economic growth for the year 2018," Soraya Sainz de Santamaria said on Friday.
Sources close to the Catalan government said Puigdemont and his team were working on an answer to Rajoy though they declined to say what line he would take.
The CUP statement echoes the position expressed late on Thursday by influential pro-independence civic group Asamblea Nacional Catalana which said: "Given the negative position of Spain toward dialogue, we ask the regional parliament to raise the suspension (on the declaration of independence)."
But the leader of Puigdemont's party, Artur Mas, who served as the region's president until 2016 and is still believed to influence key decisions, said on Friday declaring independence was not the only way forward.
"If a state proclaims itself independent and cannot act as such, it's an independence that is merely aesthetic," he told Catalan television TV3.
"The external factor must be taken into account in the decisions that will be made from now on," he said.
The European Union, the United States and most other world powers have made it clear they wanted Catalonia to remain within Spain.
"If we allow Catalonia - and it is none of our business - to separate, others will do the same. I do not want that," Jean Claude Juncker said in a speech at Luxembourg University.
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