But what will happen if Catalonian President Carles Puigdemont really does declare independence on Tuesday?
She said she felt no reason to have to decide whether she was Catalan or Spanish. We are facing a tremendous unknown.
In a separate rally in Madrid's Colon Square, thousands clamored for the unity of Spain and against any attempt by the northeastern region to break away.
"We are going to prevent independence from occurring".
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 the independence referendum could backfire.
The final results from the wealthy north-eastern region showed 90% of the 2.3 million people who voted backed independence.
Almost 900 people were injured as the police, trying to enforce a Spanish court ban on the vote, attempted to disperse voters.
Spanish police tried to sabotage the vote by raiding polling stations, beating voters and firing rubber bullets into the crowds.
Losing Catalonia is nearly unthinkable for the Spanish government.
Three banks as well as gas and water companies have announced plans to move their corporate headquarters out of the region, as Catalonia is plunged into a period of instability.
The stakes are high for the eurozones fourth-largest economy.
Other demonstrations - including in the Catalan city Barcelona - have also been held urging political dialogue.
The rally, created to defend the unity of Spain, was organized by the Catalan Civil Society (SCC) group, with the slogan'Let's recover our common sense!'
"Besides Catalans, there are thousands of men and women from all corners of Spain who have come to tell their Catalan companions that they are not alone", said Llosa, who took on Spanish citizenship in addition to that of his native Peru in 1993.
"If Catalonia has the strength, and the will, and the determination to become an independent country, then we could turn our country into a Mediterranean Denmark."
Almost one week after Spanish police tried to violently shut down Catalonia's vote to become independent from the country, thousands of people rallied in Madrid and Barcelona on Saturday in a more peaceful show of support and opposition.
Commenting on the possibility of applying Article 155 of the constitution of the kingdom, which will deprive Catalonia the status of autonomy, he noted: "I do not exclude absolutely nothing that the law allows". "Ideally, we shouldn't have to take drastic solutions but for that not to happen there would have to be changes".
However, Mr Rajoy ruled out using mediators to resolve the crisis and also said the issue would not force a snap national election.
He added: "I want to say something with absolute clarity - while the threat of independence is in the political landscape, it will be very hard for the government to not take these decisions".
"It's reached a turning point and we need to get actively involved in the defence of Spain's values as a nation", added 52-year-old Joaquin Penas, an off-duty cavalry colonel with a Spanish flag draped round his shoulders.
- Green Bay Packers vs. Dallas Cowboys Odds, Analysis, NFL Betting Pick
- Klitschko faces must-win bout against Fury
- India v/s Australia 1st T20
- Sessions ends transgender workplace protections
- Harvey Weinstein faced decades of sexual harassment allegations
- Musk: Tesla can rebuild Puerto Rico power grid
- Windows Insiders get access to mobile Microsoft Edge and Launcher app
- Best ways to make your website stand out from the rest
- Review of Plarium's Browser MMO Game Stormfall: Age of War
- Pennsylvania congressman Tim Murphy to resign