In a TV address on Wednesday night, Puigdemont said: "This moment calls for mediation".
Pique also criticized Spanish Prime Minister Mariano Rajoy for the way the government and police dealt with Sunday's plans for a referendum, which was ruled illegal by the highest rung of Spain's judiciary, the Constitutional Court.
King Felipe VI of Spain criticised the Catalonia government and did not condemn Sunday's violence.
In this Sunday, 1 October 2017 photo, Spanish National Police scuffle with people trying to reach a voting site at a school assigned to be a polling station by the Catalan government in Barcelona, Spain.
Hundreds of thousands of people took to the streets of Catalan regional capital, closing metro stations, schools and cafes and blocking roads.
It has been a part of Spain since the 15th century but has a long history of separatist sentiment. Puigdemont argues his government has been left with no choice but to proceed unilaterally as repeated attempts to discuss the matter with the Madrid government have been ignored.
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Protestors, many of them students, waved the Catalan independence flag Monday and held up signs demanding more democracy outside the headquarters of the Spanish police in Barcelona.
"If he says "as of tomorrow Catalonia will be an independent state", this will be seen as very confrontational to the Spanish Government".
The Spanish government is refusing to negotiate, while Catalonia's president previously said he was willing to go to prison over the referendum.
Catalonia's President has claimed the autonomous region will declare independence from Spain "at the end of this week or the beginning of next".
A general strike was also called in the region to protest police brutality in response to the weekend's referendum.
Almost 900 people were hurt as police violently tried to enforce a Spanish court order suspending the vote, which the government had declared illegal.
Maduro contrasted the crackdown with his own administration's handling of an unofficial July 16 opposition plebiscite, which asked voters if they wanted the national armed forces to intervene to "restore the constitutional order".