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!
Although he did not say which specific charges Mr Puigdemont might face, according to El Español, Mr Casado warned that in Spain the crimes of sedition carry a maximum prison sentence of 15 years and rebellion against the state 25 years.
It's believed he could use the opportunity to declare independence.
If the Catalans bow to pressure at the last minute and do not declare independence, Puigdemont's political survival would be in doubt.
The demonstrators defend the respect for independence in law-making in Catalonia and also unity across Spain.
Turn-out for the referendum was 43 per cent, with most residents, who wish to remain in Spain staying home.
Catalonia accounts for almost a fifth of Spain's economy, and leads all regions in producing 25% of the country's exports, CNNMoney reports.
The Catalan government had previously said it would declare independence within 48 hours of a yes vote in the referendum.
Monday meeting was suspended by the Spanish Constitutional Court to pre-empt a hypothetical push for independence.
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Barcelona police said 350,000 people gathered, while march organizers claim as many as 930,000 people turned out.
The country's courts judged the vote to be illegal and unconstitutional but the regional Catalan government made a decision to press ahead with it.
Catalans wake up on Tuesday to what could be a momentous day in their history as the world waits to see whether the region will proclaim its independence from Spain.
"There are millions of people who have voted, who want to decide.
Equally I hope the Madrid government will engage for the first time in meaningful talks - there is a lot of pressure on Madrid presently, and I think there is an opportunity for the European Union to facilitate a dialogue".
The Catalan authorities say more than 90 percent of those who voted backed secession, but opinion polls on the issue suggest the region is more closely divided.
Any independence declaration will be rejected by the Spanish government and courts, and by many people even in Catalonia, which polls shows to be nearly evenly divided on secession.
In a sign of the potential for violence, police beat unarmed voters while trying to close down polling stations during the referendum vote.
While Spanish premier Mariano Rajoy did not attend but expressed his support in a tweet, a number of heavyweights from the ruling Partido Popular, including the president of the Madrid region, Cristina Cifuentes, took part.