In a TV address on Wednesday night, Puigdemont said: "This moment calls for mediation".
The Catalan government has claimed victory in a contested referendum on independence from Spain.
Reportedly, around 900 were injured on Sunday as the riot police raided polling stations and fired rubber bullets.
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The Spanish government took a strong stance against the referendum ahead of the vote by raiding offices, shutting down pro-independence websites, and arresting officials.
In a fiery speech on Tuesday evening, Spain's King Felipe accused the Catalan authorities of "scorning" Spanish unity and threatening the stability of the whole country.
King Felipe of Spain denounced the Catalan government for destabilizing the country as the leader of the regional government repeated his intention to declare independence within days. During Spain's June friendly against Colombia in Murcia, a city in southeast Spain, he was jeered by supporters who oppose Catalonia independence.
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He said he believed advancements could be made on the issue of citizens rights. 557 MEPs backed the resolution , while 92 voted against and 29 abstained.
Puigdemont said there was now no contact between the government in Madrid and his devolved administration. Not only would it galvanise support for Puigdemont's position, it would also bring huge crowds on to the streets in protest.
"I think I can stay in the national team because I truly believe there's many people in Spain who disapprove of what happened today in Catalonia and who believe in democracy", he said.
On Tuesday, Rafael Hernando, the parliamentary spokesman for Mr. Rajoy's governing Popular Party, said the Catalan strike was "clearly political, with Nazi" connotations in terms of indoctrinating Catalans into following a separatist ideology.
The four include regional police chief officer Josep Lluis Trapero and Jordi Sanchez, the head of the Catalan National Assembly that has been the main civic group behind the independence movement.
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