Concern is mounting in Europe over a possible declaration of independence by the Catalan regional parliament and the reaction of the Spanish government, which could exacerbate what is already Spain's worst political crisis for decades.
The valley had the lowest voter turnout by far in Catalonia's October 1 independence referendum, which had been declared illegal by Spain's constitutional court.
In a TV interview on Monday, European affairs minister Nathalie Loiseau said: "If there were to be a declaration of independence, it would be unilateral, and it would not be recognised".
On the eve of the rally, Spain's Prime Minister Mariano Rajoy issued a stern warning to Catalan leaders who have said they could declare independence this week.
They were backed by the ruling People's Party (PP), the pro-government Catalan Ciudadanos party, and, at the last minute, by the opposition Socialist Party.
Mario Vargas Llosa, the Peruvian writer and 2010 Nobel Prize victor, participated in the massive demonstration that took place in Barcelona last week against Catalonia's push for independence from Spain.
Residents, some 7.5 million people, have also been able to maintain their national language: Catalan.
"We reach out for dialogue but we'll support the response of the rule of law in the face of any attempt to break social harmony".
Puigdemont will address the Catalan parliament at 6 p.m. (1600 GMT) on Tuesday on "the current political situation" amid speculation he could ask the assembly to declare independence.
"We will apply what the law says", he said, according to a partial transcript released by TV3.
Secession-minded lawmakers are meeting Tuesday in Catalonia and some say that is when they will declare independence for the northeastern region in Spain.
"I want to make one thing absolutely clear: as long as the threat of a declaration of independence remains on the political horizon, it's going to be very hard for the government not to take steps".
Catalonian officials claim the referendum results give them a mandate to create a new country. Millions of people have voted, who want to decide.
"While the [German government's] coalition talks have not even started (and are also unlikely to start before Sunday's regional elections in Lower Saxony), the German economy is powering ahead", he said.
Mr Rajoy told Catalan leaders that there is still time to backtrack and avoid Madrid taking over the region's government.
The vote was marred by allegations of police brutality.
But protesters jeered members of Catalonia's regional police force, the Mossos d'Esquadra, which had largely ignored a court order to close polling stations and seize ballot boxes during the referendum.
Some executives aren't waiting to see what happens next, and have protectively moved their headquarters out of Catalonia.