Tuesday's protest follows a call by Catalan trade unions for a general strike in Spain's northeastern region to condemn police violence, which left nearly 900 injured, during Sunday's unauthorised vote.
In a TV address on Wednesday night, Puigdemont said: "This moment calls for mediation".
'They have placed themselves totally outside the law and democracy, ' he said of the Catalan leadership.
The Catalan government announced that 90 per cent of nearly 2.3 million voters had voted in favour of independence.
More than 800 people were injured after Spanish police stormed polling stations and tried to forcibly prevent people from voting, firing tear gas and physically attacking prospective voters.
Catalan authorities said that about 90 percent of the 2.26 million people who participated in an independence referendum on October 1 voted in favor of a split from Spain.
Protesters converged on Barcelona today as Catalans observed a general strike to condemn police violence during a banned weekend referendum on independence.
Catalonia is one of the richest parts of Spain.
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He was with five-year-old Zobia Kousar who is now battling for her life in the GMC, Jammu . He said that both were killed and that soldiers recovered two weapons from the site.
Mr Puigdemont must return to the path of law before any negotiation could take place, it said said in a statement (in Spanish).
Mr. Puigdemont has said that the government of Prime Minister Mariano Rajoy is returning Spain to the authoritarianism of the former dictator, Gen. Francisco Franco.
Late Tuesday Catalonia's leader, Carles Puigdemont, told the BBC that the region will declare independence in a matter of days.
Just as Madrid will not recognise the results of a referendum both it and the courts have declared illegal, so it will not recognise an independence declaration.
The judge leading the judicial investigation, Carmen Lamela, also summoned the leaders of two prominent Catalan pro-independence civil groups: Jordi Cuixart of Omnium Cultural and Jordi Sanchez of the Catalan National Assembly (ANC).
His remarks came hours after Spain's King Felipe VI ratched up tensions by urging authorities to defend "constitutional order".
The vote has also been branded illegal as Catalonia's political leaders did not follow due political process to call the referendum, according to the Spanish government.