In a speech to regional lawmakers in Barcelona, Puigdemont stopped short of declaring an outright split but left the door to secession open, leaving some political rivals scratching their heads.
"I assume the mandate of the people for Catalonia to become an independent republic," he said.
But the 54-year-old asked the Catalan parliament to "suspend the effects of the independence declaration to initiate dialogue in the coming weeks."
After the speech, Puigdemont and other Catalan officials signed a document proclaiming "full sovereignty" for Catalonia, but it was unclear whether the document had any legal basis.
"We call on all states and international organisations to recognise the Catalan republic as an independent and sovereign state," the document read.
"We call on the Catalan government to take all necessary measures to make possible and fully effective this declaration of independence and the measures contained in the transition law that founds the republic," it added.
The central government fired back just minutes after Puigdemont's speech, with a spokesman rejecting what Madrid termed Catalonia's "tacit" independence declaration.
Spain's deputy prime minister said an emergency cabinet meeting had been called for Wednesday. Prime Minister Mariano Rajoy was also due to hold talks with Socialist opposition leader Pedro Sanchez.
Political leaders in Catalonia, Spain and Europe have come out against an independence declaration, concerned over Spain's biggest upheaval since its transition to democracy in the 1970s.
EU nations are watching developments closely amid concern that Catalan independence could put further pressure on the bloc still dealing with the fallout from Britain's shock decision to leave.
Police deployed en masse around Catalonia's regional parliament on Tuesday, blocking public access to a park that houses the building as crowds watched the session on giant screens, waving Catalan flags and some brandishing signs reading "democracy."
There were mixed reactions among those who had hoped to witness a historic moment for a region that is deeply divided over independence.
"In essence we're happy but I was expecting more," said 66-year-old Pere Valldeneu.
Merce Hernandez, a 35-year-old architect, said: "I am very emotional, this is a historic day. I'm satisfied."
At stake is the future of a region of 7.5 million people deeply divided over independence, one of Spain's economic powerhouses whose drive to break away has raised concern for stability in the European Union.
Rajoy has vowed to use everything in his power to prevent independence and has even refused to rule out imposing direct rule over the semi-autonomous region -- an unprecedented move many fear could lead to unrest.
EU President Donald Tusk also urged Puigdemont against making a decision that would make "dialogue impossible".
But the Catalan president says the independence referendum that took place on October 1 despite a court ban justifies splitting from Madrid.
Around 90 percent of those who cast ballots voted for independence. But the referendum was poorly monitored and many Catalans opposed to secession boycotted the vote, which was further marred by a violent police crackdown.
Anger on both sides
On Monday, Ada Colau, the popular mayor of Barcelona, warned Puigdemont that a unilateral declaration of independence would put "social cohesion" at risk.
Pro-unity and pro-independence supporters have staged mass rallies in Barcelona over the past week, highlighting divisions in Catalonia.
Anger over the police violence during the referendum may have swung some Catalans over to the independence camp. But both sides have come under fire for their dogged refusal to engage in dialogue.
Carolina Palles, a 53-year-old flower vendor in Barcelona's popular La Ramblas boulevard, said it was "a sad day", almost two months after the seaside city was hit by a deadly terror attack.
"Rajoy's government handled things very badly," she said, while also accusing the separatists "of persisting until the very end, like martyrs".