Mario Vargas Llosa, the Peruvian-born author known for his right-wing views, is attending the rally and has denounced Catalan independence, calling it a nationalist movement that will bring down Spain. "This crisis needs to be resolved through dialogue at all levels of Spanish politics".
The minister also reiterated Brussels' warning that an independent Catalonia would "automatically" be out of the European Union and have to reapply to join.
Some of the demonstrators took to rooftops, including families with children, and leaned over ledges from their perches overlooking the streets below to wave giant Spanish flags in a city accustomed to the prevalence of the Catalan pro-independence estelada.
Members of Puigdemont's Popular Unity Candidacy party had threatened to meet in Parliament on Monday anyway, in an act of defiance, but it is unclear if they will. It said its priority was to protect "clients, shareholders and employees" given the current political and social situation.
Monday meeting was suspended by the Spanish Constitutional Court to pre-empt a hypothetical push for independence.
The address could be the moment when Catalonia's leader declares that the region will break away.
"Many people believe - and he seems to be moving in that direction - that he will use this opportunity to declare, or to announce the results of the referendum which, as far as he was concerned, were overwhelmingly in favor of independence", Dominic Thomas, chair of the department of French and Francophone Studies, University of California Los Angeles, told CNN.
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The Madrid government, grappling with Spain's biggest political crisis since an attempted military coup in 1981, made it clear that it would respond immediately to any such unilateral declaration.
The sides dug in as the clock ticked down to a Tuesday evening session in the regional parliament where separatists have called for an independence declaration, a plan that has raised concerns for stability in the European Union.
After an illegal referendum over independence was held last Sunday, several companies chose to move their headquarters away from this Spanish northeastern region.
The October 1 vote has been followed by mass protests of Catalans angered by police violence as authorities tried to stop the vote and, more recently, by others in Catalonia and Madrid urging the unity of Spain.
That shocked even many Catalans who were opposed to independence and sparked angry demonstrations against the police.
Around 900 people were injured when officers used rubber bullets and batons against voters at polling stations.
"If it [independence] happens, I'll immediately branch out to the Catalan clubs in the League", Tebas said in an interview with Spanish broadcaster Gol TV.
Until this weekend, Rajoy has remained vague on whether he would take the unprecedented step of triggering Article 155 of the constitution, the so-called nuclear option which enables him to sack the regional government and call a local election. In that case, they would also lose the right to do business across the EU.