The most serious threat to Spain's national unity in decades is likely to come to a head in the coming days with attention focused on whether Catalonia will make good on its promise to declare independence - and what form that declaration may take if it comes to pass.
Catalan authorities say more than 90% who voted backed independence, although opinion polls suggest it is much closer.
If Catalan leader Carles Puigdemont declares the region independent as promised, possibly by Tuesday, Spain will face its greatest political upheaval since its return to democracy in the 1970s.
The motion passed by the SNP conference acknowledges that the Catalan and Spanish governments are "perfectly entitled to take positions for and against independence".
On Sunday, hundreds of thousands of pro-unionists protested in Barcelona against the referendum.
The building was later guarded by local police. The vote has not benefited from the guarantees usually required (electoral commission, assessors, electoral lists, public, secret ballot, etc.), making it unlikely the recognition by the 28 independence of Catalonia proclaimed on this basis.
Careful not to undermine Rajoy, the European Union has merely called for dialogue between the sides.
Some European officials are also anxious that any softening in Spain's stance towards Catalan independence could fuel secessionist feelings among other groups in Europe such as Belgium's Flemings and Italy's Lombards.
Spain's Prime Minister Mariano Rajoy could suspend the existing autonomous status that Catalonia enjoys under the country's system of regional governments.
Mr Rajoy told Catalan leaders that there is still time to backtrack and avoid Madrid taking over the region's government.
"I urge the Spanish government and the regional government of Catalonia to renew their commitment to a resolution through dialogue", the former United Nations chief added.
Barcelona police said 3,50,000 people participated, while march organisers Societat Civil Catalana claimed that 9,30,000 people turned out.
With its own language and cultural traditions, demands for independence in Catalonia date back centuries but have surged during recent years of economic hardship.
Catalonia accounts for almost a fifth of Spain's economy, and leads all regions in producing 25% of the country's exports, CNN Money reports.
Catalonia's top judicial official, meanwhile, ordered additional Spanish police protection for the headquarters of the regional judiciary.
Dozens of protesters surrounded two Mossos vans and called the officers standing on guard in front of them "traitors".
However, there is a belief that breaking away is a long shot.
Puigdemont is due to address the Catalan parliament on Tuesday about the "current political situation", and many expect him to declare the region's independence as a result of the 1 October referendum. But less than half of the region's electorate voted, and the way the referendum was held has raised a host of complaints about its legality and validity.
In clearer terms, on Sunday a member of PdeCat, one of the parties in the ruling coalition government in Barcelona, Marta Pascal, told the BBC the nationalists would stop short of issuing a unilateral declaration of independence on Tuesday.