Spain is bracing for more protests on Saturday despite tentative signs that rival sides may be seeking to defuse the crisis after Madrid offered a first apology to Catalans injured by police during their outlawed secession vote.

Catalan leaders had threatened to declare secession unilaterally and Spanish Prime Minister Mariano Rajoy vowed to stop them, rejecting calls for mediation in a dispute that has drawn cries of concern even from Barcelona and Real Madrid footballers.

Spanish media reported that pro-secession parties in Catalonia's parliament were working on a declaration of independence for Tuesday.

Spain's deepest political crisis in decades has raised fears of further unrest in the northeastern region, a tourist-friendly area of 7.5 million people that accounts for a fifth of Spain's economy.

READ MORE: How would a Catalan secession affect FC Barcelona?

Opponents of secession have called for demonstrations around Spain and a major rally in Barcelona on Saturday.

Also Saturday, people who support dialogue to end the crisis plan to gather in a bid to pressure mayors nationwide.

The anonymous initiative, which spread across social media, seeks to promote talks using the slogan: "Spain is better than its leaders."

"It's the moment to come together to tell (our leaders) that they are incapable and irresponsible," the group's manifesto reads. The gathering will start from around midday (10:00 GMT).

A "patriotic" march will start around the same time in central Madrid, organised by people who support a united Spain.

Friday saw the first signs the sides may be willing to step back from the brink in a political conflict that risks destabilising Europe.

After days of ill-tempered rhetoric, the central government said it regretted the injuries and suggested Catalonia should hold a regional election to settle the crisis.

Catalan government minister Santi Vila, a close of ally of regional President Carles Puigdemont, meanwhile told broadcaster Rac1 that his side could consider a "ceasefire" in the dispute, to avoid a further crackdown by Madrid.

Businesses and the government kept up economic pressure on Catalonia however, with several big companies announcing moves to shift their legal domiciles to other parts of Spain.

'We deeply regret'

Puigdemont postponed an appearance in the regional parliament at which some leaders were hoping for a declaration of independence, a spokesman said - gaining time and easing tensions. It was unclear what he planned to say at the session.

Spain's central government apologised on behalf of police to people hurt in last Sunday's referendum disturbances.

"I can do nothing but regret it, apologise on behalf of the officers who intervened," said the government's representative in Catalonia, Enric Millo.

READ MORE: Spain king 'ignoring millions of Catalans': Puigdemont

Central government spokesman Ignacio Mendez de Vigo also said later he "regretted" the injuries.

"It would be good to start mending this fracture ... through regional elections," he told a news conference.

In Madrid meanwhile, Catalonia's police chief and two prominent separatist leaders avoided being remanded in custody at a court hearing on Friday over sedition accusations.

The court summons raised tensions, but, despite the gravity of the accusations, the court did not issue a custodial order that could have further escalated the dispute.

Spain's Constitutional Court on Thursday ordered the suspension of a session scheduled for Monday in the Catalan parliament at which some leaders have called for an independence declaration.

If Catalonia declares independence, Spain could respond by suspending the region's existing autonomous status and imposing direct rule from Madrid.