But Mr Puigdemont in his declaration to parliament called for Catalonia's independence to be suspended pending negotiations with Madrid.
Rajoy, speaking after an emergency session of his ministerial team on Wednesday, said the cabinet had agreed to issue a formal request to the Catalan government in Barcelona for confirmation of whether it has declared independence.
Following his declaration to Parliament, Puigdemont and his allies signed an Independence declaration outside the chamber, but its legal validity was unclear.
Puigdemont said on Tuesday that he had accepted "the mandate of the people for Cataloniato become an independent republic" following a banned referendum earlier this month.
In a much anticipated address to the Catalan Parliament on Tuesday night, President Puigdemont said: "We call on worldwide states and organisations to recognise the Catalan republic as an independent and sovereign state".
ON TUESDAY NIGHT, Catalan President Carles Puigdemont announced that he had signed a declaration of independence - however, he suspended implementation of the declaration to allow for negotiations to take place with the Spanish Government in the coming weeks.
Prime Minister Mariano Rajoy has vowed to do everything in his power to prevent the region's Independence in a dispute that has hurled Spain into its deepest political crisis in decades.
But the speech pleased financial markets, boosting the euro on hopes that his gesture would mark a de-escalation of Spain's worst political crisis since an attempted military coup in 1981.
Spain has been in turmoil since a disputed referendum on October 1 which was declared invalid by the country's Constitutional Court.
The question of Catalan independence, the Spanish Government's handling of the situation, and theEuropean Union's response were running themes at the SNP conference this week, with a topical resolution passed by members expressing support for the Catalan people in the face of police violence.
Ahead of Puigdemont's address on Tuesday, influential figures including Barcelona's Mayor Ada Colau and European Council President Donald Tusk had urged him to step back from declaring independence.
Around 90 per cent of those who cast ballots voted for Independence but the poll was poorly monitored and many Catalans opposed to secession boycotted it.