Thousands of demonstrators g Antonio Masiello/Getty Images

The potential constitutional crisis facing Madrid has not gone away and could reach a decisive point this week, despite a mass protest in favor of a united Spain on Sunday. Hundreds of thousands of people took to the streets in Catalonia Sunday to call for unity, voicing their opposition to last week's non-binding and referendum on independence on October 1 that was declared illegal by the Spanish government and constitutional court. Police in Barcelona estimated that 350,000 people had attended the march while Societat Civil Catalana, an anti-independence group that organized the protest, put the number of demonstrators at 930,000. Waving both Spanish and Catalan flags, demonstrators on Sunday praised the actions taken by the Spanish government to prevent the symbolic referendum vote, and criticized local politicians who have encouraged secession from Spain.

Responding to the latest pro-unionist march in Catalonia, Raul Romeva, the region's foreign affairs minister, told CNBC on Sunday that there had been a larger pro-independence response from the Catalan people and that needed to be addressed by Madrid. "For six to seven years in a row we have seen millions of people on the street. I'm not talking about governing, I'm talking about society. We have seen millions of people on the street demanding to approach, politically, that issue. I think that the people deserves, they have earned the right to be listened (to)," he said. "Obviously from that perspective we have been trying to have that dialogue to engage with the Spanish government, unfortunately we are alone at the table. So in order to have a negotiation or dialogue you need a counterpart and so far we are alone at the table and you need two to tango," he added.

Puigdemont to address regional parliament

Sunday's protest centered in the regional capital Barcelona and will likely put more pressure on the regional government to drop its claims to independence. The vote saw 90 percent of the 2.28 million people who voted choose independence. Voter turnout was low at 43 percent, however, although the regional government said 770,000 potential voters were not able to vote following the Spanish police's crackdown on voters and polling stations. Spanish Health Minister Dolors Montserrat, who originates from Catalonia, delivered a brief statement at the rally on Sunday: "Today is a very important day for all the Catalans and today we are going to put a stop to the independence, and we will … And we want to build for the Catalans and with all the rest of the Spanish people, this grand nation and this great democracy all together." The government in Madrid has urged its counterpart in Barcelona to resist declaring independence although Prime Minister Mariano Rajoy has rejected calls for mediation to resolve the impasse with the Catalan government.

Catalan President Carles Puigdemont has said he will address the regional parliament on Tuesday evening and it's still uncertain whether he will go ahead with declaring independence — as he stated last week — particularly after a strong show of support in favor of unity with Spain. Rajoy said Madrid could use its constitutional powers to suspend Catalonia's autonomy and prevent it from declaring independence. In an interview with the El Pais newspaper published on Sunday, the Spanish leader suggested he could trigger article 155 of the constitution, which would allow him to dismiss the regional government and call fresh local elections. He said he would not "rule out anything that is within the law."

Firms to relocate

Amid the uncertainty, a number of Spanish companies headquartered in Catalonia, including banks Sabadell and Caixabank, have opted to relocate due to fears over secession. Meanwhile, Spanish energy company Gas Natural and water firm Agbar have announced moves to Madrid. The decisions to relocate likely dealt a blow for the Catalan government and comes after ratings agency Moody's said in a report Friday that Catalan independence would have "broad negative, albeit highly uncertain, credit implications for a wide range of bond issuers in Spain and the region."