CUP, a radical left and pro-separatist party that helps to secure the Catalan government's absolute majority in the regional parliament, wants to take the jump.
"It is now time for the next step - declare independence," said CUP parliamentarian Carles Riera in a press conference on Friday
But some, even within the government, are worried that the consequences of declaring independence might be too big and that a better solution would be to mediate with Madrid.
In Catalonia there has been an increased call for dialogue to avoid a final clash between Barcelona and Madrid. A lawyers' association supported by several institutions and organisations met with Puigdemont and other government officials on Friday afternoon. However, an expected press conference following the event never took place.