His equivocal position seemed created to appease the most fervent separatists, but also to build support -both in Catalonia and internationally - by provoking another tough response from Rajoy's Cabinet.
If Mr Puigdemont confirms by Monday that he has, he will be given a further three days to withdraw the declaration.
Spain is preparing to celebrate its National Day amid a continuing political crisis sparked by Catalonia's disputed independence referendum.
Catalonia is once again interested in holding talks, because we strongly believe that present conflict can be resolved, Puigdemont said, after regretting that both in the past and in the present they will not find out interlocutors to their sovereign claims.
The independence speech made by Catalonia's leader was a "trick", Spanish Foreign Minister Alfonso Dastis said on Wednesday, although he said there was room for negotiations within the frame of Spain's constitution. He said he refused to engage in dialogue with a disobeying Catalan government. Article 155 has never been used before.
Carles Puigdemont's speech to the Catalan parliament on Tuesday was "a trick to say one thing and do the opposite", Dastis told French radio station Europe 1.
Rajoy said his government had asked the regional government to clarify whether or not it had declared independence.
This would begin with a Cabinet meeting and a warning to the regional government to fall into line.
"There is an urgent need to put an end to the situation that Catalonia is going through - to return it to safety, tranquillity and calm and to do that as quickly as possible", Mr Rajoy said.
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Speaking later in parliament, Rajoy said Spain was facing the most serious threat to its 40-year-old democracy.
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.
The leader of the opposition Socialist Party, Pedro Sanchez, backed Rajoy's demand for clarification in order to "get out of the swamp".
The drive to break Catalonia away from Spain has raised concern for stability in a European Union still coming to terms with Britain's shock decision to leave the bloc.
About 2.3 million Catalans - or 43 percent of the electorate in the northeastern region - voted in the independence referendum.
According to news media, among the measures taken by Rajoy to tackle down secessionist challenge is an eventual intervention of Catalonia's autonomy through the application of Article-155 of the Constitution.
Catalonia, one of Spain's wealthiest regions, has seen several major companies announce plans to move their head offices elsewhere because of the crisis.
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