"The cabinet has agreed this morning to formally require the Catalan government to confirm whether it has declared independence after the deliberate confusion created over whether it has come into effect", he said in a television address on Wednesday.
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.
"(Puigdemont's) first reaction has been to insist on establishing a "bilateral dialogue" with Spain with "no prior conditions"; backpedalling on independence would only lead to an even bigger disappointment within the secessionist camp", he said in a note Wednesday.
The legal validity of the declaration was unclear.
The deadline set the clock ticking on Spain's most serious political emergency since its return to democracy four decades ago.
This requirement is a necessary step before triggering Article 155 of the constitution, which would allow Madrid to suspend the region's political autonomy.
"There is no mediation possible between democratic law and disobedience, illegality", he told parliament.
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Catalan officials say nearly 90% of voters backed independence with a turnout of 43%.
The European Commission has said it supports efforts to promote unity in Spain and again called for full respect for the constitutional order in that country.
Catalan lawyers, civil society groups and politicians in Catalonia and elsewhere in Spain have offered to mediate between the two sides, but the prime minister rejected the offers while thanking those who made them.
But Spain's economic strains during the world's financial crisis, coupled with resentment that the region pays more in taxes than it receives in investments and transfers from Madrid, have helped push the cause of secession from the fringes of Catalan politics to centre stage.
Rajoy will also appear in the Spanish parliament on Wednesday to talk about the Catalan issue.
"It is not peaceful, it is not free, it will not be recognised by Europe and now everyone knows it will have costs", he told lawmakers.