Some 90% of Catalans who voted in a disputed referendum on Oct.1 backed independence.
IG analyst Chris Beauchamp says a positive beginning of the week for the Spanish Ibex 35 index suggests investors are confident there will be a resolution to the crisis.
On the eve of the rally, Spain's Prime Minister Mariano Rajoy issued a stern warning to Catalan leaders who have said they could declare independence this week.
European Economics Commissioner Pierre Moscovici, asked about the economic impact of the Catalan debate, said the Spanish constitutional order must be respected.
Mr Casado was later careful to point out that his comparisons with Mr Companys had referred to the Catalan's 1934 trial and incarceration after the independence bid, not to his subsequent capture, torture and execution by General Franco's police in 1940.
Spain also sought to reassure global investors concerned about the political situation in the country. "I don't think it will be better at all, because they want to take the country outside the European Union and outside of Spain".
Catalonia, a northeastern region about the size of Belgium, is home to 7.5 million people and accounts for a fifth of Spain's economy.
The Catalan parliament could declare independence from Spain on Tuesday evening, claiming legitimacy from the "yes" vote that came from the illegal ballot on 1 October.
"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 at the University of California Los Angeles, told CNN.
Recent polls had indicated that Catalans are split on independence, though leaders said police violence during the referendum turned many against the state authorities.
Puigdemont hinted in an interview on Sunday that the region would go ahead with the declaration if Madrid continued to refuse dialogue.
But the Spanish Government, buoyed by Sunday's protests in Barcelona, the Catalan capital, made it clear on Monday it would respond immediately to any such vote.
Despite the outrage, Rajoy and Spanish King Felipe VI defended the police and doubled down on their stance to take whatever measures necessary to keep Catalonia from seceding. Scenes of Spanish police beating unarmed voters in the October 1 referendum caused worldwide shock.
Mr Rajoy told Catalan leaders that there is still time to backtrack and avoid Madrid taking over the region's government.