Catalan separatists signed what they say is a document declaring independence.
Puigdemont immediately asked the Catalan Parliament for the implementation of independence to be suspended for a few weeks to open a period of dialogue.
He added: The only way to go forward is democracy and peace, that means to respect people who think differently. That requires dialogue.
Spanish Prime Minister Mariano Rajoy, after an emergency Cabinet meeting last night, demanded that Puigdemont clarify whether independence has been declared.
Deputy Prime Minister Soraya Saenz de Santamaria earlier said the Catalan leader doesnt know where he is, where he is going and with whom he wants to go.
She said the Government couldnt accept the Catalan Governments validation of its referendum law because it is suspended by the Constitutional Court, or the results of the October 1 vote because it was illegal and void of guarantees.
Puigdemont was under pressure to back down after the European Union strongly supported Spain.
His pleas for the EU to mediate between Barcelona and Madrid fell on deaf ears, with Brussels insisting the referendum was illegal and that it was an internal matter for Spain.
Earlier EC President Donald Tusk addressed him directly in a speech in Brussels: The force of arguments is always better than the argument of force. Today I ask you to respect - in your intentions - the constitutional order and not to announce a decision that would make such a dialogue impossible.
Right up to the start of his speech, Puigdemont received requests not to go ahead with the declaration.
Threats by banks and local businesses to pull out of the region, as well as pro-unity demonstrations in Barcelona, may have helped convince Puigdemont to step back from the brink.
Catalonia is a European issue, Puigdemont said, adding that the EU should defend its democratic values after seeing how Spanish security forces had behaved. This was the first time in Europe that an election took place with the police beating people as they tried to cast their vote.
Puigdemonts announcement sparked scenes of celebration outside the regional parliament in the streets of Barcelona, where thousands had gathered to watch on a giant screen.
Xavier Turo, a 45-year-old electrician, travelled from the village of Sentmenat with his wife to watch.
We are nervous, but happy. We have been waiting a long time for this. Our government is risking their necks for us.
What are the options for Spain and Catalonia?
1. The Spanish Government could use some of the various legal means at its disposal to overrule the Catalan authorities. Prime Minister Mariano Rajoy's Popular Party has a majority in Spain's Senate, the chamber which must approve the triggering of Article 155 of the Constitution, allowing central government to take over regional institutions if they are breaking the law.
2. The Rajoy Government seeks a majority in Congress to declare a state of emergency. Carles Puigdemont and his government colleagues are arrested.
3. Rajoy agrees to negotiations mediated by the European Union, something he has previously ruled out. If there are talks, Catalonia's Government would ask for normality to return to the region, including the withdrawal of around 10,000 extra police officers sent there by Madrid in the referendum build-up. Talks would focus on constitutional reform.
4. President Puigdemont could call a fresh election in the Catalan Parliament, either because he sees little or no progress from talks, or if he fails to maintain unity among his slender majority of pro-independence forces. The result could establish whether a majority of Catalans are in favour of secession.
5. Little change. Catalan authorities continue to act under the supposed legality of Catalonia's Parliament and laws which pave the way towards an independent state. Catalan officials are steadily accused, charged and eventually put on trial for rebellion.
- Telegraph Group Ltd, AP