Demonstrations are planned in the capital Madrid and other cities, with supporters calling for a similar rally in Catalonia's capital Barcelona.
Meanwhile, Spain's government representative in Catalonia earlier apologised to those hurt during police efforts to stop the referendum.
But Enric Millo blamed the Catalan government for holding an illegal vote.
In the first apology by a Spanish government official over the violence during the referendum, Mr Millo said he could not help but "regret it and apologise on behalf of the officers that intervened".
Hundreds of people were injured as police, trying to enforce a Spanish court ban on the vote, attempted to seize ballot boxes and disperse voters.
Meanwhile, Catalan foreign affairs chief Raül Romeva told the BBC his government would go ahead with an independence debate in parliament.
"Parliament will discuss, parliament will meet.
"Every attempt the Spanish government has used to impede things to happen, they have been demonstrated completely not only useless but counter-productive," Mr Romeva said.