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.
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.
According to the Catalan government, a majority of those who took part in the illegal referendum voted for the separation of the region from Spain.
In recent weeks, a stream of Catalonia-based firms and banks have moved their legal bases outside the regionas a crisis over a Catalonian push for independence from Spain deepened.
Although it is not know what Puigdemont might say, any declaration of independence from the region would likely lead to more violence.
"I'm calling on the sensible people in the Catalan government. don't jump off the edge because you'll take the people with you".
Turnout was 43 percent as Catalans who reject independence largely boycotted the poll.
Spain last week also apologised for the violent scenes seen last weekend during the unofficial referendum.
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At Sunday's rally, demonstrators cheered and applauded when a national police helicopter flew over and some people shook the hands of national police officers to thank them for their efforts to stop the referendum.
"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.
Hundreds of thousands of Spaniards rallied Sunday in a tide of red and yellow national flags in what is the worst upheaval since the country returned to democracy in the 1970s.
Careful not to undermine Rajoy, the European Union has merely called for dialogue between the sides.
European Affairs Minister Nathalie Loiseau said the crisis following the banned October 1 referendum had to be resolved through dialogue within Spain, BBC reported.
"They do not want to get embroiled in a messy confrontation or encourage separatist movements".
Catalan President Carles Puigdemont had been expected to make a formal declaration at a specially convened session of the Catalan parliament on Tuesday.
"Ultimately, he will probably be forced to continue with the existing pattern of confrontation and escalation".