The demonstrators defend the respect for independence in law-making in Catalonia and also unity across Spain. It is not yet clear if he will declare the restive region's independence from Spain, and whether such a declaration would be purely symbolic.
"The unity of Spain can not be voted on or negotiated - it must be defended", read one sign in the crowd.
However, he is under pressure to hold off from secession plans, which would escalate what is already the biggest political crisis Spain has experienced since a 1981 failed military coup.
"It is expected that Puigdemont will on Tuesday say an independence bid in the future will be considered, which is a dramatic step back from expectations last week that a deceleration of independence is imminent".
"If independence were to be recognised - which is not something that's being discussed - the most immediate outcome would be that [Catalonia] automatically left the European Union".
However, on the eve of Tuesday's parliamentary session, neither Prime Minister Mariano Rajoy nor Catalan leader Carles Puigdemont showed signs of entering into talks, with each buoyed by large protests on both sides of the independence divide.
Nathalie Loiseau, France's minister for European affairs, warned Monday that "if there were a declaration of independence it would be unilateral and it wouldn't be recognized".
Sunday's anti-independence demonstration, which included Catalans and people from other parts of Spain, underlined how the dispute has riven the region itself.
The premier noted that 4,000 additional police were deployed in Catalonia in the run-up to the referendum, adding they would stay until the crisis was over.
"Applying 155 would involve a lot of things because it's not been studied very much", she told Cope radio.
During the event, Vargas Llosa said that though nationalism is wreaking havoc in the region right now, Spanish democracy is here to stay, and no plot for independence can destroy it. Catalonia's independence referendum on October 1 was declared illegal by Spanish Prime Minister Mariano Rajoy. Rajoy assured Catalan leaders that there "is still time" to backtrack and avoid triggering a tough response from the central government in Madrid. The index on Friday fell 0.4% (http://www.marketwatch.com/story/european-stocks-slip-with-us-jobs-data-in-view-spanish-banks-resume-selloff-2017-10-06) but posted a weekly gain of 0.3%.
"I hope that nothing will happen".
"Absolutely not", he said. "We'll do everything that legislation allows to ensure that".
"What we are seeing playing out in Catalonia is the strategic use of secrecy via technology to imagine and enact a different kind of politics", says Dr Clare Birchall, senior lecturer in contemporary culture at Kings College London who writes on secrecy and surveillance argues this represents a new, radical form of secrecy.
They were backed by the ruling People's Party (PP), the pro-government Catalan Ciudadanos party, and, at the last minute, by the opposition Socialist Party. "The consequences are very hard to predict".
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