Spanish Prime Minister Mariano Rajoy, a conservative who has taken a hard line on Catalan independence faces a huge challenge to see off the issue without further unrest and potential damage to his minority government.
Mr Puigdemont said he would file a complaint against Spanish police who fired rubber bullets, smashed into polling stations and beat back protesters.
Catalonia's leader said 90% of voters backed independence from Spain, but the central government has vowed to stop the wealthy northeastern region - which accounts for a fifth of Spain's economy - from breaking away, dismissing the poll as a "farce".
The European Commission said Monday that "violence can never be an instrument in politics" but did not make any other allusion to the violence during the vote.
Catalonia continues to take steps toward a unilateral declaration of independence.
Some have criticized the European Union for "double-standards", saying its talk of upholding democratic values appeared hollow given its opposition to the public vote on independence.
"No society should accept a status quo it doesn't want, against its will, through force and beatings, and this can only be resolved with democracy", Puigdemont said. The Spanish state, he went on, needed to ensure constitutional order and the rule of law in Catalonia, the richest region of Spain.
Puigdemont called on Madrid to remove its police forces, which Catalans criticized as having overreacted on Sunday, and said that he would open an investigation into their actions.
"The Spanish government is letting political opponents be arrested, it is influencing media and blocking Internet sites".
Earlier on Wednesday, Spanish members traded accusations over whether leaders in Barcelona or Madrid were responsible for the crisis.
Officials estimated voter turnout for Sunday's referendum was about 42.3 percent of 5.34 million eligible voters.
A total of 893 people were injured in clashes with police attempting to thwart the public from voting last weekend.
Without specifying when, Carles Puigdemont, who heads all three branches of the Catalan government, said he would submit the result for approval to the regional Parliament. "Some have tried to break the rule of law, and we have answered with serenity and sanity".
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. The strike was called in protest against "the grave violation of rights and freedoms" during Sunday's ballot which was declared illegal by the Madrid government. Yet ultimately, who outside of Spain would be ready to give the necessary global support to a Catalan state? The EU, she said, should mediate a solution to the crisis.