In a much anticipated address to the Catalan Parliament on Tuesday night, President Puigdemont said: "We call on global states and organisations to recognise the Catalan republic as an independent and sovereign state". Lauren Frayer reports from Barcelona.
The Catalan government said 90 percent of those who voted backed independence but turnout was only 43 percent as many opponents of independence stayed at home.
Puigdemont demands the withdrawal of national police from Catalonia and calls for worldwide mediation.
Puigdemont says his government is preparing to proclaim independence, perhaps at "the end of the week".
But on Wednesday morning, the Spanish stock market rose 1.16 percent on hopes for a breakthrough in the crisis.
He later told Spain's parliament the Catalan government had until Monday, Oct 16 at 0800 GMT to answer.
Banco Sabadell, Catalonia's second largest bank, announces it will relocate its offices outside the region.
Puigdemont delays an appearance in the regional parliament until Tuesday.
Tens of thousands of people, some dressed in white, demonstrate in several Spanish cities, as well as the Basque Country, demanding dialogue to resolve the crisis. "Yesterday I tried to send a message of calmness and to remind people that we are facing a political problem that we need to solve with politics and not with police", he said.Hundreds of people were injured in Catalonia on October 1 as Spanish national police sought to prevent the referendum going ahead.
Over 350,000 people, according to local police, join a unity march in Barcelona. If Puigdemont was to confirm he did declare independence, he would be given an additional three days to rectify it, until Thursday, Oct 19 at 0800 GMT.
On the same day that Catalonia's president called for negotiations with Spain to secure independence for his state, the White House signaled it favored talks between Catalonia and the Madrid government and "them moving forward". It was like he declared independence and then abruptly took it back.
However, he added, the region would suspend the process of declaring independence in a bid to establish a constructive dialogue with Madrid.
Crisis talks will be held in Spain on Wednesday after Catalan leaders suspended a declaration of independence on Tuesday in favor of dialogue with Madrid.
Catalan President Carles Puigdemont signs a declaration of independence at the Catalan regional parliament in Barcelona, Spain, October 10, 2017.