Spain's Constitutional Court had earlier suspended the Catalan parliament session that had been planned for Monday - though it remains scheduled, according to Catalan officials. "I can tell you with absolute frankness that it will not happen", Rajoy said.
"We feel both Catalan and Spanish", Araceli Ponze, 72, said as she rallied in Barcelona.
While thousands of Spaniards manifest for the "dialogue" and " the unit", the Spanish head of government is expressed for the first time on Sunday in a big Spanish newspaper, since the beginning of the crisis last October 1. They say 90% voted for independence, but have not published the final results.
The focus has now shifted to Tuesday, when Puigdemont is set to address the regional parliament "to report on the current political situation" in Catalonia. Catalan lawmakers were meeting Friday afternoon to discuss the request.
But the pro-dialogue rally almost clashed with a large pro-unity demonstration in Plaza de Colon where thousands of people carried Spanish flags and some danced around a fountain, before police separated the two groups. Spanish officials insist the referendum didn't count because the courts forbade it. Catalonia's leaders, however, maintain that the vote was valid and will stand.
"They must finally sit down with one another and talk, things can not keep on like this", said a man that came to Saturday's protest with his daughter on his shoulders. Videos on Sunday saw police yanking voters and others by their hair and kicking and hitting them.
The prosperous and powerful northeastern regional Catalan government says it plans to declare independence from Spain, creating Spain's gravest constitutional crisis in decades.
Some bankers and their customers were privately nervous about the Catalan situation.
When asked if he had unleashed forces now beyond his control that could lead to civil unrest, and see Government MPs arrested and detained, Mr Mas said, "Well I hope this scenario won't happen in Catalonia".
CaixaBank, another large Barcelona-based institution, is considering a similar move.
The prospect of an exit has sent shivers among business heavyweights, including lender Banco Sabadell and energy giant Gas Natural, who were among the firms to green-light relocations of their registered address.
"We like how things have been up until now and want to go on like this".
There has already been a business backlash following the result.
Thousands took to city squares of Madrid and Barcelona calling for talks to diffuse Spanish and Catalonian tension, amid Catalonia's threat to secede. The four are to be questioned again in coming days.
The support given in public statements by European Union leaders to Rajoy is combined with concern expressed in private about how the Spanish government's use of police to prevent Catalans from voting last week in an independence referendum could backfire.
Meanwhile, the Catalan chief of police, Josep Lluis Trapero, has appeared before a judge in Madrid on suspicion of sedition against the state.