Spanish Prime Minister Mariano Rajoy said on Sunday he would not rule out suspending Catalonia's autonomous status in the event it claimed independence , marking the premier's first remarks since last week's controversial referendum.
On Sunday, hundreds of thousands of pro-unionists protested in Barcelona against the referendum. "If this gentleman unilaterally declares independence, measures will have to be taken".
On Sunday, Josep Borrell, a Catalan former president of the European Parliament, called on Puigdemont not to "push the country towards the cliff".
Turnout figures were impressive, but were still lower than what was achieved by the pro-independence camp in an October 3 general strike, when 700,000 people took to Barcelona's streets, according to Guardia Urbana estimates.
"On the other hand if the politics between Spain and Catalonia don't go well it would signify support from England for Catalonia and that would not be welcomed internationally".
Around 350,000 people attended the rally, municipal police said, while organisers put turnout at between 930,000 and 950,000.
Protesters, some of whom arrived via bus or train from other parts of Spain, marched peacefully.
Mr Puigdemont is set to address the Catalan parliament on Tuesday, and although it remains unclear what he plans to say, many secessionists are urging him to declare unilateral independence.
But it expresses concern that any state would "seek to deny people's right to democratically express their will" and condemns the violent attempts by Spanish police to stop the referendum going ahead.
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But now the tide seems to be turning.
"If there were a declaration of independence it would be unilateral and it wouldn't be recognised", Nathalie Loiseau said on CNews digital news channel.
The slogan for the Barcelona protest, which was organised by the Societat Civil Catalana, the main anti-independence group in Catalonia, was Enough, let's recover good sense!
Catalonia, which has its own language and culture and is led by a pro-independence regional government, held a referendum on October 1 over secession in defiance of Spain's constitutional court, which had declared the vote illegal.
Catalan authorities say the "Yes" side won the referendum with 90 percent of the vote, though only 43 percent of the region's 5.3 million eligible voters turned out in polling that was marred by police raids of polling stations on orders to confiscate ballot boxes. He said this includes the use of Article 155 of the Spanish Constitution, which would allow the central government to take control of the governance of a region "if the regional government does not comply with the obligations of the Constitution".
"The ideal scenario would be that there were no need for drastic solutions, but for that there would need to be rectifications".
With the crisis deepening, and no sign of an end to political instability, some Catalan businesses have announced they are relocating their headquarters to other parts of Spain to avoid the possibility of getting knocked out of the European Union common market by a Catalonian secession.
However, asked if he was ready to do so, Rajoy told El Pais newspaper on Saturday: "I don't rule out anything that is within the law".