Puigdemont insisted yesterday that "the majority of Catalan people want Catalonia as an independent state" but Rajoy dismissed Puigdemont's push as "a fairytale".
The deadline set the clock ticking on Spain's most serious political emergency since its return to democracy four decades ago.
He demanded that the regional government clarify whether it now considered itself independent following a speech by Puigdemont on Tuesday night during which he said that he would proceed with the secession but would suspend it for a few weeks to facilitate negotiations.
Reports in Spanish media have suggested that if the Spanish Prime Minister were to activate Article 155 in the absence of a response from the Catalan president, pro-independence parties in the Catalan parliament would then declare independence.
"There is no mediation possible between democratic law and disobedience, illegality", he told parliament. This requirement is prior and obliged to implementation of any of measures that Executive may adopt under article 155 of Constitution. He said this includes the use of Article 155 of the Spanish Constitution, which would allow the central government to take control of the governance of a region "if the regional government does not comply with the obligations of the Constitution".
"If the Spanish state repeats its actions and enforces the clause, we will be in full confrontation with the state", Rivas said.
Those who opposed the referendum had said they would boycott the vote.
Rajoy's government previously had refused to grant Catalonia permission to hold a referendum on the grounds that it would only poll a portion of Spain's 46 million residents and was therefore unconstitutional.
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He added that he was willing to negotiate on the issue of regional autonomy and changes to the constitution - but this had to be within the framework of the law.
Opposition Socialist leader Pedro Sanchez offered a compromise of sorts.
Catalonia is one of Spain's wealthiest regions but a stream of companies has announced plans to move head offices out of the province in response to the crisis.
Many Catalans have long highlighted the region's differences from the rest of Spain but the latest surge for independence began in 2010, when Spain's top court struck down key parts of a charter that would have granted Catalonia greater autonomy and recognized it as a nation within Spain.
In an interview with German newspaper Die Welt, Mr Rajoy said that Spain will not be divided.
Lauren Frayer, reporting for NPR from Barcelona, spoke to graduate student Eugenio Juliá, who "is paying close attention because he's anxious the terms of his grad school scholarship might change if Catalonia leaves Spain and the European Union", Frayer says.
The stakes are high - losing Catalonia, which has its own language and culture, would deprive Spain of a fifth of its economic output and more than a quarter of exports.
EUGENIO JULIA: I think it was not very straightforward.